Lab Manual Upes Physics
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PROFESSIONAL
PHYSICS LAB MANUAL FOR Engineering Students (Semester 1)
Name........................................................................................... Branch.................................Roll No........................................... Institute.......................................................................................
Department of Physics
College of Engineering Studies University of Petroleium and Energy Studies, Dehradun 2014 -1st Ed. Revised
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PROFESSIONAL PUBLICATIONS 154, HOUSING BOARD COLONY, AMBALA CANTT - 133001 MOB. 98962-31633 PROFESSIONAL PUBLICATOINS, 98962-31633
INSTRUCTIONS FOR LABORATORY •
The objective of the laboratory is learning. The experiments are designed to illustrate phenomena in different areas of Physics and to expose you to measuring instruments. Conduct the experiments with interest and an attitude of learning.
•
You need to come well prepared for the experiment
•
Work quietly and carefully (the whole purpose of experimentation is to make reliable measurements!) and equally share the work with your partners.
•
Be honest in recording and representing your data. Never make up readings or doctor them to get a better fit for a graph. If a particular reading appears wrong repeat the measurement carefully. In any event all the data recorded in the tables have to be faithfully displayed on the graph.
•
All presentations of data, tables and graphs calculations should be neatly and carefully done.
•
Bring necessary graph papers for each of experiment. Learn to optimize on usage of graph papers.
•
Graphs should be neatly drawn with pencil. Always label graphs and the axes and display units.
•
If you finish early, spend the remaining time to complete the calculations and drawing graphs. Come equipped with calculator, scales, pencils etc.
LIST OF EXPERIMENTS No.
EXPERIMENT
PAGE NO.
To determine the wavelength of sodium light (monochromatic light) by Newton’s rings method. To determine the wavelengths of the mercury (blue, green/ yellow y1, y2) light by normal incidence method, using diffraction grating.
5
3.
To determine the specific rotation of cane sugar solution with the help of Polari-meter.
12
4.
To determine the resistance per unit length of a Carey foster’s bridge wire and then to determine the specific resistance of the given wire.
15
5.
To determine the energy band gap of PN junction semiconductor diode in reverse biased.
20
6.
To determine the energy band gap of a semiconductor using four probe method.
23
7.
To study the Hall Effect and hence determine the hall coefficient (Rh) and carrier density (n) of a given semiconductor materials.
26
8.
To determine the (1) numerical aperture (NA), (2) power losses due to macro bending and adaptor of given optical Fiber.
30
9.
To study the V-I characteristics of p–n junction diode and to calculate resistance of a diode in forward and reverse bias.
33
10.
Laser Diffraction method for single slit experiment.
37
11.
Study of both the current–voltage characteristic and the power curve to find the maximum power point (MPP) and efficiency of a solar cell
41
12.
To determine the wavelength of sodium light with the help of Fresnel’s biprism
46
13.
To determine the dispersive power of a material of prism using spectrometer.
51
1. 2.
8
55-56
Index
PROFESSIONAL PUBLICATIONS AMBALA CANTT.
PROFESSIONAL’S Physics Lab Manual - I
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EXPERIMENT NO. 1 AIM: To determine the wavelength of sodium light (Monochromativ Light) by Newton’s rings method. APPARATUS: Optical arrangement for Newton’s rings, traveling microscope, sodium lamp, short focus convex lens, reading lens and spherometer. PRINCIPLE & FORMULA: Consider a Plano-convex lens of large radius of curvature placed on a circular plane glass plate. A thin film of air is formed between the glass plate and the lens as shown. At the point ‘O’ where the lens is in contact with the glass plate, the thickness of the air film is zero and as we proceed away from O, the thickness of the film gradually increases. At the points around ‘O’ and at equal distance from it, the thickness of the film is same since the bottom surface of the lens is spherical.
Figure 1.1 Now suppose that monochromatic light is incident normally on the air film at X at a distance of ‘a’ from ‘O’. This light is partially reflected at the top surface of the air film at ‘X’ and after refraction in air partially at ‘Y’. The two reflected beams will have certain path difference depending upon the thickness of the film (XY). Interference of these two reflected beams takes place which can be observed through a microscope placed vertically above the lens. The point X will be bright or dark, depending upon whether the path difference is odd or even number of half wave length of incident light. Similarly interference of light occurs at all other points of the film and a set of rings which are alternately bright and dark will be observed with a dark spot at the centre of the rings. Each ring is the locus of all points in the film which are at the same distance from the centre O of the ring system. If dm and dn are the diameters of the mth and nth dark rings respectively and R is the radius of curvature of the curved surface of the Plano-convex lens, it can be shown that the wavelength of light is given by λ
d 2m d n2 4R m n
Thus by forming these rings called Newton’s rings and by measuring their diameters, the wavelength of light can be determined. APPLICATIONS • Thickness of a thin film. • Radius of curvature of convex surface of the given lens. • Refractive index of a liquid. • Wavelength of a monochromatic light. • Color separation scanning Equipments/ Colour scanners. • Anti Newton ring Glass in photographic industry.
PROFESSIONAL’S Physics Lab Manual - I
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PROCEDURE: 1. Place the Plano-convex lens on the circular plane glass plate such that the convex surface of the Planoconvex lens is in contact with the plane glass plate. Place this combination in the wooden box, which contain a plane glass plate inclined by 45o to the incident light from the short focus convex lens. Place the wooden box under the traveling microscope and adjust it until sharp rings are seen. 2. Bring the point of the cross wires to the centre spot of the ring system. Starting from the centre of the ring system move the microscope cross wires to the left up to the 19th dark ring. (This number selected arbitrarily). 3. Set the vertical cross wire tangential to the 19th dark ring at the left and note the reading on the horizontal scale of the microscope. Repeat the same for alternate dark rings until cross wire reaches 1st dark ring. Similarly take the readings of alternate rings at the right side starting from 1st ring. 4.
Determination of radius of curvature of the convex surface of the Plano-convex lens (R) Take out the lens and mark the surface which was in contact with glass plate. Place the spherometer on the convex surface of the plano-convex lens and note the reading of the spherometer (h1) then place the spherometer on the plane glass plate and note the reading (h2). Reading of the spherometer for convex surface of the lens (h1) =……cm Reading of the spherometer for plane glass plate (h2) =……cm Average distance between the legs of the spherometer (l) =……cm Height of the convex surface (h) = (h1 – h2) =……cm Radius of curvature of the curved surface of the Plano-convex lens R
l2 h ...................................cm 6h 2
TABLE
Left side (L)
Right side (R)
Diameter d=L ~ R (cm)
Microscope Reading (cm) S.No.
Ring No.
d2 (cm2)
1
20
2
18
3
16
4
14
5
12
6
10
7
8
8
6
9
4
10
2
PROFESSIONAL’S Physics Lab Manual - I
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GRAPH
d
2 m
m
d 2n
n
Y
Diameter 2
Draw a graph with the ring number on X-axis and (diameter)2 on Y-axis. By joining the points a straight line passing through the origin is obtained as shown in figure 1.2. Find the slope of the straight line, which is:
d2m
2
dn
CALCULATIONS
O
Radius of curvature of the plano convex lens (R) Diameter square of the mth ring d2m Diameter square of the nth ring d2n Slope of the straight line Wavelength ( )
=……cm =……cm2 =……cm2 =……cm2 =……cm
n m number of ring
Figure 1.2
RESULT: Wave length of Sodium light ( ) is found to be =……cm = ……. A A0 PRECAUTIONS 1. 2.
The lens surface as well as circular glass plate must be well cleaned. The centre spot of the ring system should be dark.
VIVA-VOCE 1. 2. 3. 4. 5.
What is Newton’s Ring? How are these rings formed? Why are these rings circular? If the fringes are not exactly circular what do you infer? Why are you using the Plano-convex lens of large focal length? Why do the rings get closer as the order of rings increases? Why is the centre of these rings dark?
REFERENCES 1 Practical Physics – Gupta.Kumar 2 A text book of Practical Physics – R.K Goel.Govind Ram 3 B.Sc Practical Physics – C.L Arora
X
PROFESSIONAL’S Physics Lab Manual - I
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EXPERIMENT NO. 2 AIM: To determine the wavelength of the spectral lines (Blue, Green, Yellow, Y1, Y2) by using diffraction grating the normal incidence method. APPARATUS: Spectrometer, diffraction grating, sprit level, mercury vapor lamp and magnifying lens. PRINCIPLE & FORMULA Diffraction is the phenomenon of bending of light around the obstacle specially when passed close to sharp edges or through apertures or narrow openings. Consider a plane transmission grating with alternate opaque and transparent lines. Let a parallel beam of light rays are incident normally on the grating. Most of these rays are transmitted in the direction of the incident light through transparent portions of the grating and if a converging lens is placed in their path, they are brought to focus at O. there will be a very bright image. Some of the incident light is diffracted at the edges such as B, D and F etc., at different angles as shown in figure 2.1. If we consider these rays (bend at B and D at an angle from the direction of the incident light) all such rays form a parallel beam and after passing through the lens, they are brought to focus at I. The intensity at I will be maximum or minimum depending upon the path difference between the diffracted rays from B and D. If‘d’ is the grating element (distance between two consecutive lines on the grating), path difference is equal to d sin .
I B
O
D F
Figure 2.1
Thus if d sinq = nl (an integral number of wave lengths) the bright images are formed in the focal plane of the lens. These are called first order, second order (n=1, 2, 3,) etc., images. Thus one set of images will be formed on one side of the central bright image at O. also the diffraction or bending of light rays takes place to the other side of the incident direction and corresponding images of different orders are formed on the other side of the central image O. Thus in the field of view of a telescope of which the lens L forms the objective, a central bright image and the diffracted images of different orders (n=1, 2, 3, etc.) are observed. If the incident light is monochromatic, each order of diffracted image will be of the same color, but if white light (mercury) is incident on the grating, each diffracted image consists of a whole spectrum. Thus spectra of different orders are formed on either side of the central white image. APPLICATIONS • Grating as filters • Fiber optic telecommunication • Beam splitters
PROFESSIONAL’S Physics Lab Manual - I
• • • • • • •
9
Optical couplers Metrological Ground-based astronomy Raman spectroscopy Colorimetry Atomic and molecular spectroscopy Fluorescence spectroscopy
Source Slit
FORMULA
a b sin n Or
=
Collimator
Grating equation
(a b)sin n
o 45o 90
45o
Where
Grating
(a + b) = grating element = angle of diffraction. n = order of diffraction
Telescope
Prism table
Figure 2.2
PROCEDURE 1. 2.
3.
4.
Make preliminary adjustments of the spectrometer. Clamp the grating on the prism table with the help of a clamp. Adjust the grating for normal incidence position by the following method. I. Set the telescope for direct reading position and note the reading V1 and V2. II. Add 90o to the above reading and rotate the telescope to this reading and fix it. III. Now rotate grating until the image of the slit is at cross wires of the telescope and fix the prism table. Now the incident light is making 45o with the grating plane (See figure 2.2). IV. Release the vernier scale knob and rotate the vernier scale through an angle of 45o so that the grating maintains exactly normal to the incident light. Fix the vernier table in this position; now grating is at normal incidence position. Release the telescope and rotate it to left side of the direct reading position until the I order spectrum is seen. Now coincide the vertical cross wire over the spectral lines of desired color and note down the readings in the two verniers as V1 and V2. Further, rotate the telescope till II order spectral lines are visible, coincide the cross wire and note down the readings in two verniers as V1 and V2 against 2nd order. Now rotate telescope to the right side of the direct reading position until the first order spectrum is seen. Concide the cross wires with the same yellow spectral line and note down the readings in the two verniers as V1 and V2. Rotate the telescope further until the II order spectral lines are seen, then coincide the vertical cross wires with lines and note down the readings as V1 and V2. The angle of diffraction is given by half the angle between corresponding lines.
CALCULATIONS No. of lines per cm on the grating = grating element = a + b = 1/N =
2.54 15000
PROFESSIONAL’S Physics Lab Manual - I
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Figure 2.3 TABLE Order of diffraction
Spectral lines
I order
Blue Green
II order
Y1 Y2 Blue Green
Spectrometer Readings Left Right V1 V1 V2 V2
V V1 V2 V2 2 1
a b sin
2
n
Y1 Y2 RESULT: The observed wavelengths are given in table Colour of specturl line
(observed)
Blue Green Yellow 1 Yellow 2
........ ........ ........ ........
(Standard) ........ ........ ........ ........
PRECAUTIONS 1. Optical adjustment of the spectrometer should be made directly. 2. The slit should be as narrow as possible. 3. Grating surface should not be touched with fingers as the slit might get damaged. 4. The grating should be exactly normal to the incident beam. 5. While taking observations, telescope and prism table should be kept fixed.
% (Error) ........ ........ ........ ........
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VIVA-VOCE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
What is a plane transmission diffraction grating? Why the grating should be kept normal to the plane of grating, then which formula should be applied? What is (a+b) in the formula? How many orders of spectra do you get here? Why do you not get the third order spectrum? How many types of grating are known to you? What is the main difference between the spectrum obtained by grating and due to prism? What do you mean by dispersion of light? Why a light on passing through the prism disperses into its constituent colours? Define dispersive power of any material? On what factors does the dispersive power depend? What is the angle of deviation?
REFERENCES 1 2 3 4 5 6
Practical Physics – Gupta.Kumar A text book of Practical Physics – R.K Goel.Govind Ram B.Sc Practical Physics – C.L Arora Engineering Physics- M.N Avadhanulu, A.A Dani and P.M Pokley A Laboratory Manual of Physics – D.P Khandelwal B.Sc Practical Physics – Harnam Singh
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EXPERIMENT NO. 3 AIM: To determine the specific rotation of cane sugar with the help of a polarimeter. APPARATUS: Half-shade/Bi-quartz polarimeter, light source, sugar, measuring flask, beaker, analytical balance and a weight box. PRINCIPLE & FORMULA If a beam of unpolarised light is viewed through two crossed Nicol prisms (when the principal planes of the two are perpendicular to each other) the field of view is completely dark. The first Nicol is called the polariser and the second is called the analyzer. If the sugar solution is introduced between the two crossed Nicols, it is found that light is restored in the field of view. To extinguish the light, the analyzer has to be rotated through a finite angle depending on the concentration of the sugar solution. This experiment shows that the substance introduced between the Nicols has rotated the plane of polarization. Such substances are called optically active substances and the phenomenon is called ‘Optical activity’. If the plane of polarization is rotated clockwise, the substance is called dextro-rotatory (right handed) and if it is rotated anti-clockwise, the substance is called levorotatory (left handed). The angle by which the plane of polarization is rotated is directly proportional to the length of the path traveled by the light in the substance (l), the concentration of the substance (c). It also depends on the temperature and wavelength of light. Thus for a particular wavelength and temperature l c or
Slc
or
S
v lc lm
Where S = specific rotation or specific rotatory power of the substance = rotation produced in degree m = mass of sugar in gm. dissolved in water v = volume of sugar solution l = length of the tube in decimeter Specific rotation, for a given wavelength at a given temperature, is defined as the rotation produced by one decimeter length of the solution having a concentration of 1 gm/cc. APPLICATIONS • Sugar Industry • Chemical Industry
• Pharmaceutical Industry • Flavours, Fragrances and Essential Oils
LAURENT’S HALF - SHADE POLARIMETER Laurents half shade polaririmeter is the instrument used for finding the specific rotation of certain optically active solutions. The essential parts of a Laurent’s half-shade polarimeter are shown in the figure. ‘S’ is unpolarised/ ordinary source of light and L is a convex lens which renders the incident light into a parallel beam. N1 and N2 are two Niclo prisms. N1 acts as polariser while N2 acts as analyzer. N2 can be rotated about a common axis of N1 and N2. The rotation of analyzer (N2) can be read in a graduated circular scale (S.C.). The vernier is also provided to read the fraction of a degree. Light after passing through polariser becomes plane polarized with its
PROFESSIONAL’S Physics Lab Manual - I
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vibrations in the principal plane of the Nicol (N1). The plane polarized light now passes through a half-shade device (H.S.) and then through a tube ‘T’ containing the optically active substance. Usually ‘T’ is a hollow glass tube having a large diameter in the middle so that no air bubble may be in the path of light when filled with a liquid. The emergent light on passing through analyzer N2 is viewed through a telescope T. The telescope is focused on the half shade. S L
N1
HS
T
N2
SC
lens
polariser
halfshade
tube
analyser
circular scale
T telescope
PROCEDURE 1. 2.
3. 4.
5.
Weight exactly 4 gms of sugar and dissolve it in 100 c.c. of distilled water in a measuring flask; make the solution exactly 100 c.c. If the polarimeter is employing a half shade device, a monochromatic source is used and if bi quartz device is used than white light can be used. Clean the tube such that it is free from dust and fills it with distilled water and close the ends. Place the tube in position inside the polarimeter. look through the telescope and rotate the analyzer till the two halves of the field of view appear equally bright. Take the reading of main scale as well as vernier scale and find out the total reading (1). Take out the tube and fill it completely with the sugar solution so that there are no air bubbles in it. (Do Not Over Tight the Cap It May Break the Tube) Close the tube, place it in its position in the polarimeter and look through the telescope. Again set the field of view as explained in step-3. Note the reading of the analyzer on the circular scale (2). Repeat step 4 of the experiment for different concentrations of the solution and tabulate the observations.
OBSERVATIONS Least count of the vernier of the circular scale Length of the cylindrical tube (l) Mass of the sugar dissolved (x) Volume of the solution (v) Temperature of the solution (T) = room temperature
= ……. ° = …….cm =……. gm =……. cc. =……. o C
TABLE S.No.
Concentration of solution (x/v) gm/cc
Reading on circular scale when two halves are of equal intensity xn
1.
Air/plain water
x1
2.
4/100
x2
3.
8/100
x3
4.
12/100
x4
Angle of rotation of plane of polarization θ = xn - x1
S=
10.θ. v l .x
PROFESSIONAL’S Physics Lab Manual - I
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Y
GRAPH Plot a graph between concentration of the solution (c) on the X-axis and angle of rotation of the plane of polarization of plane polarized light () on the Y-axis. You get a straight line passing through the origin. CALCULATIONS
slope
S = Where
θ The specific rotatory power c
Concentration, c (in gm/cc)
X
slope 10 l l is the length of the tube in cm Reading with distilled water, say 1 = …….
RESULTS: The specific rotation of glucose solution at …oC for the given light is _______________degree/unit concentration/unit length. PRECAUTIONS 1. 2. 3. 4.
The window cap of the tube containing the solution should be gently tight, so that there will be no leakage. There should be no air bubble in the solution contained in the polarimeter tube. The temperature of the solution must be recorded (room temperature). Having set the analyzer in correct position w.r.t the polarizer, turn the former through 180o and again make a similar setting. 5. Under no circumstances the polarizer should be touched during one complete set of observation. 6. Use sodium light for half shade, and white light for bi-quartz.
VIVA-VOCE 1. 2. 3. 4. 5. 6. 7. 8.
What do you mean by polarization of light? How does polarized light differ from ordinary light? What is angle of polarization? What are the plane of polarization and plane of vibration? What is Polaroid? What are the uses of Polaroid’s in daily life? What is Brewster’s law? What is the polarizing angle for the air-glass?
REFERENCES 1 2 3 4 5 6 7
Practical Physics – Gupta.Kumar A text book of Practical Physics – R.K Goel.Govind Ram B.Sc Practical Physics – C.L Arora Electronics fundamentals and applications – Ryder, J.D Properties of silicon and germanium – Conwell,E.M Engineering Physics- M.N Avadhanulu, A.A Dani and P.M Pokley A Laboratory Manual of Physics – D.P Khandelwal
PROFESSIONAL’S Physics Lab Manual - I
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EXPERIMENT NO. 4 AIM: To determine the specific resistance of a given wire by using Carey-Foster’s Bridge. APPARATUS USED: Carey-Foster’s bridge, Battery Eliminator , zero centre galvanometer, decimal resistance box, thick copper strips, given experimental resistance wire, a rheostat of range 10 to 20, plug-key, jockey, connection wires and screw gauge. FORMULA USED: For Resistance per Unit length of bridge wire (ρ):The standard resistance box R.B. for X in G1 and thick copper strip for shortening so that Y=0.
(i)
The resistance per unit length of bridge wire is given by;
X /cm l2 l1
where X = known fractional resistance value resistance box. l1 is the balancing length with X in G1 and Y in G4 (before Interchanging ) l2 is the balancing length with X in G4 and Y in G1 (after Interchanging) (ii)
For the unknown Resistance: The unknown resistance (Y ) of the given wire is given by; R = Y = X - (l’2 – l’1) where Y(R) is the unknown resistance of the given wire connected in G4 and G1 X is the value of resistance in the decimal resistance box connected in gap G and G the outer gap. 1 4 l’1is the balancing length with X in G and Y in G (before interchanging) 1 4 l’2 is the balancing length with X in G and Y in G (after interchanging) 4 1 ρ = resistance per unit length of the bridge wire. The specific resistance S of the wire is given by: R A r2 Y S ohm-cm l l where, S = specific resistance, r = radius of wire in cm l = length of wire in cm, Y = resistance of the wire in ohm.
(iii)
CIRCUIT DIAGRAM
known resistance X
G1
E
K
P
Q
SR
SR
G2
G3
unknown resistance Y E : Battery Eliminator, K – Key P,Q : Standard Resistance in G2 and G3 respectively.
G4
X : Variable resistance from Resistance Box Y : Unknown resistance for which S is to be determined.
J W1
l1
G
W2
G : Galvanometer, J : Jockey
Figure 4.1: Carey Foster’s bridge for determining specific resistance
PROFESSIONAL’S Physics Lab Manual - I
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PROCEDURE The experiment is done in the following three steps; (a) Measurement of Resistance per unit Length ( ρ ) of the Bridge Wire:Calibration of the Bridge Wire. For this step, set up the following experimental set-up; (i)
Press the Jockey J at the two ends of the wire W1 and W2. If the deflections in galvanometer are opposite the circuit connections are correct.
(ii)
Plug out 0.1 ohm of resistance in X (in G1). Check for the opposite deflections. Then find the point exactly where the deflection is becoming zero by moving the jockey. This point is the balancing point.
(iii)
Note the distance of null deflection point from the positive end of wire W1 to get the balancing length (l1)
(iv)
Repeat this process by changing X values from 0.1 ohm to 0.5 ohm and note down the corresponding values of l1.
Calculate the value of linear resistance or resistance per unit length of bridge wire ρ for each set of observations by the following formula and find the average value of .
R l2 l1 and then find its mean.
(b) Measurement of unknown resistance of the given wire: (i)
Connect the circuit as shown in figure 4.1. Remove the copper strip from the gap G4 and connect the given unknown resistance wire of nearly 50 cm length.
(ii)
Introduce a suitable resistance of nearly 1-3 ohm in the decimal resistance box x in gap G .
(iii)
Slide the jockey on the wire till you get a balancing point. Note balancing length l’1 from left end W1 of the wire.
(iv)
Interchange the positions of resistance box and unknown resistance wire. Again get the balance point by sliding the jockey on the wire and note the balancing length l’2 from W1.
(v)
Repeat this experiment for different values of resistances from the resistance box and get other values of (l’2-l’1).
(vi)
The unknown resistance is given by the formula:
1
R Y X (l '2 l '1 )
where X is the resistance introduced in the resistance box and l2 l1 is the difference of the two balancing lengths before and after interchanging the R.B. and unknown resistance in each case and find the value of unknown resistance. (c) For specific resistance: (i)
Measure the length of the unknown resistance wire in cm.
(ii)
Measure the diameter of the given resistance wire by screw gauge at few places and then calculate mean value of diameter and hence radius; r = d/2
PROFESSIONAL’S Physics Lab Manual - I
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OBSERVATIONS Table for the determination of linear resistance of Bridge Wire ( ρ ) S.
Resistance (ohm)
Balancing Length (cm)
No.
X
Before
After
Interchanging X in G1 (l1)
Interchanging
Y
1
0.1
0
2
0.2
0
3
0.3
0
4
0.4
0
5
0.5
0
X in G (l2)
Linear l2–l1
Resistance
(cm)
4
X /cm l2 l1
(ii) Table for the determination of unknown resistance of a given wire: S.
Resistance (ohm)
Balancing Length (cm)
No.
X
Y
Before
After
l'2–l'1 Y X (l 2 l1 )
(Known)
(Unknown)
Interchanging
Interchanging
(cm)
X in G1 (l'1)
X in G (l'2)
1 2 3 4 5
0.5 1.0 1.5 2.0 2.5
4
Y Y Y Y Y Avg Y = ........
The unknown resistance of the wire is Y = ……… (iii) Table for the measurement of radius of wire by using screw guage Error Correction
=......... =.........
S. No.
P.S.R. (mm)
H.S.C Observed
Corrected
1 2 3 Average Diameter : …………….mm Radius of the wire, r = d/2= …………..mm =……….cm
H.S.C. L.C. TR = P.S.R + H.S.C L.C (mm) (mm)
PROFESSIONAL’S Physics Lab Manual - I
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CALCULATIONS (a) The resistance per unit length of the bridge wire is given:
R l2 l1 (Similarly calculate for other observations and take the mean)
(b) The unknown resistance of the given wire is given by;
Y=X ρ l2 l1 =....... ohm. (Similarly, calculate Y for other observations and take the mean) (c) The specific resistance of given wire is given by; S
R r2 ............ohm-cm l
RESULTS 1. The resistance per unit length of wire = ...........ohm / cm 2. The specific resistance of the material of the wire = ...........ohm-cm Measured value (S)exp
Standard value (S)
(ohm-cm)
(ohm-cm)
th
Percentage Error Sexp - Sth Sth
×100
PRECAUTIONS 1. 2. 3. 4. 5. 6. 7. 8.
The end of the connection wires should be cotton free, clean and must be tightly connected. See that the resistances in four arms P, Q, X and Y of the bridge must be of the same order so that the bridge remains quite sensitive. Continuous current should not flow in the wire otherwise it gets heated up and its resistance may undergo a change. For this, the jockey should not be dragged continuously all along the length of the wire but should be tapped at different points on the bridge wire. The bridge wire should be uniform in cross-section. The jockey should be gently put on the wire and not pressed hard to avoid and change in the diameter of the wire. The diameter of the wire must be measured in two perpendicular directions and at many places and then mean value of it must be used. A high resistance should be used in the circuit to measure the exact balancing point. (conventionally)
APPLICATIONS: 1. Compare two nearly equal resistance 2.
Determine the temperature coefficient of resistance .
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VIVA-VOCE 1. Ans.
2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. Ans. 14. Ans. 15. Ans. 16. Ans.
17. Ans. 18. Ans. 19. Ans. 20. Ans. 21. Ans.
What is the principal of Carey Foster’s Bridge? It is based on the principle that when resistance of outer gaps are interchanged, there is shift in the position of balanced point. The difference between the resistance of bridge wire between these two balance point. P X Q Y In what respect it is an improvement over Meter Bridge? How does the accuracy of resistance per unit length of the wire ( ) depend on the difference between the known resistances in the outer gaps? What can be the maximum value of this difference which you can take? When will your apparatus be most sensitive? What is the material of the bridge wire? Why it has been selected? What would you prefer, a copper strip or a copper wire in the outer gap? Why? What does represents? Will it be same at every point of the bridge wire? What is the effect of increasing the effective length of Bridge wire? What is the basic construction of a Resistance Box? Why is the wire doubled inside the box? What is the percentage composition of the alloys constantan and Manganin of which resistance wires are made? What do you mean by the resistance of a conductor? The ratio of the potential difference between the two ends of a conductor to the current flowing in it, is called the resistance of the conductor. On what factors does it depend? Resistance of a conductor is directly proportional to its length (l), inversely proportional to the area of cross section (A). It also depends upon the nature of material and temperature of the conductor.(R= kl / A). What is its unit? Unit of resistance is ohm. What is specific resistance? What is its unit? Specific resistance of a substance is defined as the resistance material having unit length and unit area of cross section RA S if A= 1 and l =1 then S = R l Its unit is ohm-cm Is specific resistance same for all materials? No, it is different for different material. What is effect of temperature on resistance? It increases with increase in temperature. What is the effect of increasing the effective length of a Carey Foster’s bridge wire? It will increase the accuracy of the result because then percentage error in reading the position of the balance point is very much decreased. What is the minimum difference resistance that you can measure with its bridge wire? It is equal to the resistance of the bridge wire. What is the maximum difference in resistance that you can measure with this bridge wire? It is equal to the resistance of the total length of the bridge wire
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EXPERIMENT NO. 5 AIM: To determine the energy band gap of a semiconductor using a junction diode. APPARATUS:Power supply (DC-3 Volts fixed), Micro ammeter, electrically heated oven, Thermometer, Semiconductor diode (OA 79). Formula Used: A graph is plotted between logs Is and (103 /T) that comes out to be a straight line. Its slope is calculated. Band gap, ΔE, in electron volts, is given by ΔE =
slope of the line eV 5.036
APPLICATIONS One of the most important applications of diodes is in the design of rectifier circuits, clipper, clamper, voltage multiplier, comparator, sampling gates and filters. THEORY A semi-conductor doped or undoped always possesses an energy gap between its conduction and valence bands. For conduction of electricity a certain amount of energy is to be given to the electron, so that it goes from the valence band to the conduction band. This energy so needed is the measure of the energy gap ΔE between the two bands. When a p-n junction is reverse biased as shown in Fig. the current through the junction is due to minority carriers i.e. due to electrons in P section and holes in N section. The concentration of these carriers depends upon the energy gap ΔE. The reverse saturated current Is value is function of the temperature of the junction diode, and varies according to the following relation: V Vp log I s log A e N n N p n exp e E kT Pp N n
Where Nn = density of electrons in N material Np = density of holes in p material Vp = velocity of holes Vn = velocity of electrons A = area of the junction k = Boltzmann Constant T = Absolute temperature of junction 3/2
Nn
Np
2 2 mn kT e h3
2 2 m p kT e h3
3/2
P
N
Figure 5.1: Reverse biasing of a PN junction
…. (1)
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mn is the mass of the electron and mp is the effective mass of hole. For small range of temperature relation (1) can be put as,
3 log Is constant 5.036E 10 T
......(2)
Obviously therefore, if a graph is plotted between log Is and 103/T, a straight line would be obtained. Where the slope of this line = 5.036 ΔE Here ΔE is in electron volts. PROCEDURE 1. 2.
3.
Plug the mains lead to the nearest main socket carrying 230V 10% at 50 Hz A.C. Insert the thermometer and the diode in the holes of the oven (The hole near to the meter is for diode OA-79) Plug the two leads to the diode in the socket, Red plug in red socket and black plug in black socket. Make the connections as per figure 5.2. (i) Now put the power ON/OFF switch to ON position and see the jewel light is glowing. Figure 5.2: Circuit diagram (ii) Put the OVEN switch to ON position and allow the temperature to increase up to 90°C. Note: As soon as the temperature reaches 95°C switch off the oven enabling the temperature to rise further and become stable around 90°C When the temperature becomes stable start taking readings of current and temperature. The current readings should be taken in steps of 5μA. The readings should be taken during fall of temperature from 90°C downwards. (iii) Tabulate readings in the form shown below: TABLE
Reverse saturation current in I s ( A )
Temperature in oC
Temperature T (oK)
103/T
log Is
(iv) Plot a graph between the readings of 103/T on X-axis and log Is on Y- axis. The graph should come as a straight line cutting both the X-axis and Y- axis. (v) Now determine the slope of the line. After determining the slope of the line calculates the Band Gap as follows: ΔE =
slope of the line =……eV 5.036
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PRECAUTIONS 1. 2. 3.
The maximum temperature should not exceed 95°C. Bulb of the thermometer and the diode should be inserted well in the oven. Silicon diodes should not be used with the set ups as in that case the temperature needed is 125°C, and the oven thermometer provided will not stand to this temperature.
VIVA-VOCE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
What do you mean by energy band gap? How are the bands formed in the solids? What do you mean by valence band, conduction band and forbidden band? How do you differentiate between a conductor, an insulator and a semiconductor in relation to the energy gap? What do you mean by intrinsic and extrinsic semiconductors? Why semiconductors behave as an insulator at zero degree Kelvin? What is a P-N junction? What is an n-type semiconductor and p-type semiconductors? What do you mean by forward and reverse biasing of a junction diode? What are the positions of holes and electrons in the two semiconductors (p-type and n-type) before contact? What is a depletion layer? What is the order of thickness of depletion layer? What are the approximate values of band gap in case of conductor, insulator and semiconductor? How does the resistivity changes with the change of temperature?
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EXPERIMENT NO. 6 AIM: To study the resistivity of semiconductor of different temperatures and also to determine the energy band gap of a semiconductor (germanium) using four probe method. APPARATUS: Probe arrangement, Sample (Germanium), Oven, Four Probe set - up, Thermometer etc. FORMULA USED: The resistivity of the semiconductor crystal which is given by:
0
where 0
f W/ S
V 2 S I
where f (W/S) is a fraction which can be known for table given with the semiconductor. S is the distance between probes. W is the thickness of semiconductor crystal. V and I are the voltage and current across and through the crystal chip. The energy band gap Eg (in eV) of a semiconductor is given by: E g 2k
2.3026 log10 1/ T
where k is Boltzman constant equal to 8.6 10–5 eV/degree and T is the temperature in Kelvin. mV Probes mV Direct current source Oven
I
I
V
Sample (crystal) chip
S W
Power Supply
Oven Figure 6.1: Circuit Diagram for Four Probe Method
APPLICATIONS
Used to both characterize the material and as a process control parameter for the semiconductor manufacturing process. Resistivity of different semiconducting materials.
PROCEDURE 1. 2. 3. 4. 5. 6.
Connect one pair of the direct current source through milli - ammeter. Other pair of probes is connected to the milli - voltmeter. Place the four probe arrangement in the electric oven connected to a power supply. Fix up a thermometer in this arrangement. Switch on the constant current source and adjust the current to a particular suitable value say 2 mA. Go on measuring the inner probe voltage V for different temperatures.
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OBSERVATIONS Current (I) Distance between probes (S) Thickness of the crystal chip (W) S. No.
Temperature (°C)
1. 2. 3. 4. 5. 6. 7. 8. 9.
20 30 40 50 60 70 80 90 100
Voltage (Volts)
= …. mA (constant) = …. mm = …..mm TABLE Temperature ρ 0 ρ (ohm cm) (°K) (ohm cm) 293 303 313 -------
1/T × 103
Log10 ρ
3.41 3.30
CALCULATIONS Find resistance corresponding to temperature in K using:
0 f W/ S
ohm-cm
where 0
V 2 S .........ohm cm I
For different 'V' calculate 0 and hence in ohm cm. Find (W/S) and then corresponding to this value choose the value of function f (W/S) from the following table; TABLE: For f (W/S) function corresponding to W/S geometry of the crystal S.No. W/S
f (W/S)
S.No. W/S
f (W/S)
S.No. W/S
1. 2. 3. 4.
13.863 9.704 6.391 5.9
5. 6. 7. 8.
2.780 1.504 1.223 1.094
9. 10. 11.
0.100 0.141 0.200 0.250
0.500 1.000 1.414 2.000
GRAPH Now plot a graph for log10 versus 1/T 103 as presented in figure 6.2. Slope of the curve is
log10 AB 1 BC 1000 T
f (W/S)
3.333 1.022 5.000 1.007 10.000 1.00045
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2.3026 log 10 (e V) Hence band gap, E g 2k IT
1.6 1.4 1.2 1.0
AB 2k 2.303 1000 BC
A Slope of the curve =
0.8
AB BC
0.6
E g 0.396
0.4
AB eV BC
0
RESULT 1. 2.
C
0.2 10
B
20 30 1 x 1000 T(K)
40
Figure 6.2 Resistivity of semiconductor crystal at different temperatures was studied & is presented in the graph of log10 and I/T × 103. Energy band gap of semiconductor crystal Eg = ............eV Standard Eg of Ge = 0.72 eV and for Si = 1.1eV Percentage error
Standard value Observed value 100 ...........% Standard value
PRECAUTIONS AND SOURCE OF ERROR 1. 2. 3. 4. 5.
The surface on which the probes rest should be uniform. Do not exceed the temperature of the oven above 120°C for safe side. Semiconductor crystal with four probes is installed in the oven very carefully otherwise the crystal may get damaged because it is brittle. Current should remain constant throughout the experiment. Minimum pressure is exerted for obtaining proper electrical contacts to the chip.
VIVA-VOCE 1 2 3 4 5 6 7 8 9 10
What do you mean by energy band gap? How are the bands formed in the solids? What do you mean by valency band, conduction band and forbidden band? How do you differentiate between a conductor, an insulator and a semiconductor in relation to the energy gap? What do you mean by intrinsic and extrinsic semiconductors? Why semiconductors behave as an insulator at zero degree Kelvin? What is a P-N junction? What is an n-type semiconductor and p-type semiconductors? What do you mean by forward and reverse biasing of a junction diode? What is the advantage of four probe method over other methods of measuring the resistivity?
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EXPERIMENT NO. 7 AIM: To study the Hall effect and hence determine the Hall coefficient (RH) and carrier density (n) of a given semiconductor material. APPARATUS: Hall Probe (Ge Crystal) (thickness 0.4-0.5 mm); Hall Probe (InAs crystal), Hall Effect set-up (Digital mill voltmeter (0-200 mV) and constant current power supply, Electromagnet (Field intensity 11,000 ± 5% gauss), Constant current power supply. FORMULA: As shown in Figure 7.1, z is the thickness along Z-axis of the crystal. Hz is the magnetic field applied along Z axis. Current I is flowing along X-axis. Hall voltage VH is developed across the faces normal to Y-axis and x is the length of the crystal along X-axis; V H .Z V .Z volt cm A 1G 1 H 10 8 cm 3 / Coulomb where VH is in volts, I IH z IH z n amperes, Z in cm and Hz in gauss.
(i)
Hall coefficient R H
(ii)
Carrier density n
i
1 RH .q
cm 3 (where q = electronic charge = 1.6 x 10-19 C)
THEORY: An E.M.F. is set up transversely across a current carrying conductor when a perpendicular magnetic field is applied. This is called the Hall Effect.
V Eh= yH y
I Z
X
h
Figure 7.1: Sample for studying Hall effect
Z
Ix
Crystal
N S Ix mV Vh
Pole piece
Figure 7.2: Illustration of measurement of Hall Voltage
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APPLICATIONS Automotive Industry: Level/tilt measurement sensor, Throttle angle sensor automotive sensors, Crankshaft position or speed sensor, Anti-skid sensor, Door interlock and ignition sensor Transmission mounted speed sensor, RPM sensors, Distributor mounted ignition sensor etc. Electronic industry: Sequencing sensors, Magnetic card reader, Proximity sensors, Office machine sensors Adjustable current sensors, Linear feedback sensor, Multiple position sensor, Microprocessor controlled sensor, Brushless DC motor sensors etc. Aerospace Industry: Temperature or pressure sensor, Remote conveyor sensing, Remote reading sensing, Current sensors, Flow rate sensor (linear output Piston detection sensor). PROCEDURE 1.
Connect the widthwise contacts of the Hall Probe (with Ge crystal) to the voltage terminal and lengthwise contacts to current terminals of the Hall effect set-up. Now switch ‘ON’ the Hall Effect set up and adjust the current to a few (mA). Check the ‘Zero field Potential’ by changing Knob to the voltage side. This voltage is error voltage and should be subtracted from the Hall voltage reading. (i.e., when Hall probe is outside the magnetic field). Now place the Hall probe in the magnetic field. This Hall probe must be fitted in the wooden stand before placing in magnetic field so that Hall probe becomes perpendicular to the magnetic field. Switch on the electromagnet power supply by connecting the pole piece to the power supply. Now place the Hall probe (InAs) attached with Gauss-meter between the pole pieces to measure the magnetic field. Measure the Hall voltage as a function of current keeping the magnetic field constant. Measure the Hall voltage as a function of magnetic field keeping a suitable value of current as constant (This is done by placing two probes between the pole pieces and decrease the spacing between the pole piece and measure the magnetic field and Hall voltage). Plot the graph between VH and I (HZ = constant); VH and H (I = constant). Calculate the slope VH/I and VH/HZ from the two graphs and calculate Hall coefficient in two ways and determine the mean value.
2. 3. 4. 5. 6. 7. 8.
9. 10.
OBSERVATIONS Thickness of the semiconductor crystal Z = 0.5 mm =0.05 cm 1 ohm1cm1 Table – 1: Magnetic field Hz = 1000 Gauss Conductivity
S.No. 1. 2. 3. 4. 5.
Current I (mA)
Hall Votage VH (mV)
Table – 2: Current I = 5 mA S.No. 1. 2. 3. 4. 5.
Magnetic field HZ (Gauss)
Hall Votage VH (mV)
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Scale x-axis 1 cm = .....mA y-axis 1 cm = .....mV A
C
C
B
Slope= 0
Scale x-axis 1 cm = .....Gauss y-axis 1 cm = .....mV A
AB BC
Slope= 0
Current, I (mA) Figure 7.3. Plot of VH versus I
B AB BC
Magnetic field(HZ) Figure 7.4. Plot of VH versus HZ
CALCULATIONS
Slope
VH AB (From plot VH vs I), I BC (i)
V Z RH 1 Slope H Volt cm A A-1G-1 = ——x 108cm3/coul. I Hz
V RH1 Slope H HZ Mean RH
(ii)
VH AB Slope H BC (From plot VH vs HZ) Z
Z Volt cm A A-1G-1 = ——x 108cm3/coul. I
RH 1 RH 2 cm3 / coul. 2 1 19 Carrier Density n R q (q 1.6 10 ) H n
1 / cm 3 19 ( cm / coul) 1.6 10 coul) 3
RESULT The value of Hall Coefficient (RH) is ——cm3/coul. The carrier density (n) = ——/cm3.
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PRECAUTIONS 1.
The Hall probe is placed between the pole pieces (in magnetic field) such that maximum Hall voltage is generated.
2.
Current through the Hall probe should be strictly within the limit as mentioned by the manufacturer.
3.
Hall voltage developed must be measured very accurately.
4.
Magnetic field is varied gradually in steps to avoid damage to the electromagnetic coils.
VIVA-VOCE
What is the Hall Effect?
On what factor, the sign of the Hall potential difference develops?
Why is the potential difference developed when a transverse magnetic field is applied to a current carrying conductor?
How will you determine the direction of the force exerted on the charge carriers?
What is the Hall coefficient? What are its units?
REFERENCES 1
Practical Physics – Gupta.Kumar
2
A text book of Practical Physics – R.K Goel.Govind Ram
3
B.Sc Practical Physics – C.L Arora
4
Electronics fundamentals and applications – Ryder, J.D
5
Properties of silicon and germanium – Conwell,E.M
6
Engineering Physics- M.N Avadhanulu, A.A Dani and P.M Pokley
7
A Laboratory Manual of Physics – D.P Khandelwal
8
B.Sc Practical Physics – Harnam Singh
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EXPERIMENT NO. 8 AIM: To determine the (1) Numerical Aperture (NA), (2) Power Losses due to Macro bending and adaptor of givem optical fibre. APPARATUS: LED, NA Jig, D.M.M, scaled screen, adaptor, one and three meter length of optical fiber, mandrel. PRINCIPLE & FORMULA 1.The Numerical Aperture (N.A) of an optical fiber (step index) is given by
2 2 N.A. n core n clad
1 2
......(1)
sin imax or
imax sin 1 N.A.
ncore = refractive index of core, nclad = refractive index of cladding imax = acceptance angle As shown in figure 8.1, light from the end of the optical fiber ‘A’ falls on the screen BD. Let the diameter of light falling on the screen BD=W, Let the distance between end of the fiber and the screen AO=L Knowing W and L, the N.A can be calculated and substituting this N.A value in Eq (2), the acceptance angle ‘θ’ can be calculated.
......(2)
B
A Foled
imax
O
W
Optical fibre
2. Losses of power in fibre optic cable are mainly due to absorption or scattering of light with Optical fibre, macro bending and joints between cables (adaptor). This loss of power ‘P’ from input (Po) to output (PL) at a distance ‘L’, can be written as PL P0eL
N.A.=
W 1
(4L2 + W2) 2
L
D Screen
Figure : 8.1
Where ‘α’ is the attenuation coefficient in decibels (dB) per unit length. (Generally dB/KM) P 10.log10 o PL α L
PL P0
L 10e 10
APPLICATIONS • • •
Telecommunications Local Area Networks (LANs) and Wide Area Networks (WANs) Factory Automation, Premises Wiring. Fiber-optic biomedical sensors, Endoscopic imaging , Aerospace and Military Applications, Fiber optic sensors.
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PROCEDURE 1.
Insert one end of either one or three meter length optical fiber cable the LED and NA jig.. Switch on LED, then red light will appear at the end of the fiber on the N.A Jig. Turn SET P0/IF knob the intensity will increase. Arrange the scaled screen at a distance L, and then view the red spot on the screen. Measure the diameter of the spot (w). Note the measured values L and W in the table. Repeat the experiment with different distances and note the readings. S. No
L ( mm )
W ( mm )
N.A
i max
1
2
3
2.
Insert one end of the three meter length plastic optical fibre cable to the FOLED and connect another end to the power meter module. Connect D.M.M test leads to Pout, red lead to red socket and black lead to black socket respectively. Set D.M.M to 2000 mV range. Switch on LED, adjust the Set Po/IF knob to set output power of the FOLED to the value -22.0 dBm( milli decibels ) i.e., DMM reading will be 220mV, note this as PO, wind the fibre on the mandrel and note the reading as POw1, similarly for two and three turns. Note the readings as POw2 and POw3 respectively. x O/P power (dBm)
Loss due to turns (dBm)
Po0
-
P Ow1
-
( PO0 - POw1 ) =
P Ow2
-
( PO0 - P Ow2 ) =
P Ow3
-
( PO0 - P Ow3 ) =
3.
Connect one meter OF cable as given above and set D.M.M for a constant value (-120mV) and note the reading as P1. Similarly take P2 by replacing one meter cable with 3 meter cable without disturbing SET PO/If knob. Now join the 1 and 3 m cables with the adopter on shown in the figure and note DMM reading as P3.
OBSERVATIONS P1 = P2 = P3 = CALCULATIONS Take P1, P2 and P3 as shown in Fig., without disturbing the SET Po / If knob. P2 P1 2 Loss due to adopter = P3 – P1 – 3X =
Loss in one meter cable (X) =
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P1
PO
1m cable
P2 3m cable
PO
P3 1m cable
3m cable
Adapter
Figure 8.2 RESULT 1. N.A of given Optical fiber is ——————— 2. Power loss due to one turn—————— dBm, two turns —————dBm and three turns ———dBm 3. Power loss due to one meter cable—————— dBm and due to adaptor ——— dBm PRECAUTIONS 1. Gently insert the optical fiber cable is to LED by turning clockwise direction of its clinch nut. (until you feel the fiber touches the micro lens) 2. Do not push applying over force which may damage micro lens 3. Gently tight the clinch nut that holds the inserted fiber firmly. 4. Before taking reading check out fiber is free of all twists and strains. 5. Two cables must meet at the center of the adopter while taking P3 reading.
VIVA-VOCE 1. 2. 3. 4. 5. 6. 7.
What do you mean by numerical aperture? On what factors the numerical aperture depends? What do you mean by acceptance angle? On what factors the acceptance angle of the fiber depends? A fiber with high numerical aperture (NA) is preferable or not? Why? What is irradiance? What do you mean by bandwidth?
REFERENCES 1 2 3 4 5 6 7 8
Practical Physics – Gupta.Kumar A text book of Practical Physics – R.K Goel.Govind Ram B.Sc Practical Physics – C.L Arora Electronics fundamentals and applications – Ryder, J.D Properties of silicon and germanium – Conwell,E.M Engineering Physics- M.N Avadhanulu, A.A Dani and P.M Pokley A Laboratory Manual of Physics – D.P Khandelwal B.Sc Practical Physics – Harnam Singh
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EXPERIMENT NO. 9 A AIM: To study the characteristics of P–N Junction diode and to calculate resistance of a diode in forward and reverse bias. APPARATUS: Power supply, Voltmeter, Ammeter, Diode and connecting wires PRINCIPLE When a P–type material is joined with N–type, a P–N Junction is formed. The plane dividing the two zones is known as a junction. Due to diffusion, some of the electrons from N–region cross over to P–region where they recombine with holes, and holes from P–region cross over to N–region and recombine with electrons. Thus a layer is formed which is known as depletion layer or charge free region or space charge region where there is no free charges available for conduction of current. The diffusion of the electrons and holes across the junction continues till a potential barrier is developed in depletion layer which prevents further diffusion of charges. The potential barrier can be increased or decreased by applying an external bias voltage. APPLICATIONS Electronic industry • • •
Signal rectifier / Diode gates / Diode clamps Limiter / Over-voltage protection / Ionizing radiation detectors Temperature measuring / Computers to cellular phones to digital audio players.
THEORY Forward Bias: When the P-N junction is forward biased i.e., when the +ve terminal of the battery is connected to the P-side and –ve terminal is connected to the N–side, the holes from P–side are repelled by positive charges of the battery towards the junction. Similarly at the same time electrons in N–side will be repelled by negative charges from the battery towards the junction. Here battery voltage should be high to impart sufficient energy to these carriers to overcome the potential barrier at the junction and enable them to cross the junction. Hence a current start flowing after a minimum voltage called potential barrier voltage Reverse Bias: Revese biasing increases the potential barrier, there by resulting in a very little current to flow. When the junction is reverse biased i.e., when +ve terminal of the battery connected to the N–side and –ve terminal is connected to the P-side, the electrons in N–side and holes in P–side are attracted away from the junction. For sufficient negative bias, the depletion region breaks down and reverse current starts flowing across the circuit. PROCEDURE
p
RL
n
a) Forward bias: 1. 2. 3.
Connect the circuit as shown in figure 9.1. Vary the potential difference and note the corresponding current value. Draw the graph by taking potential or voltage (V) on X-axis and current (I) on Y-axis.
+
V
+ mA
+ Rheostat or POT
Figure 9.1: Forward bias
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b) Reverse bias:
n
1. 2.
+
3.
Make the connections as shown in figure 9.2. Vary the potential difference and note the corresponding current value. Draw the graph by taking potential or voltage (V) on X-axis and current (I) on Y- axis.
RL
p
V
+
+ Rheostat or POT
Figure 9.2: Reverse bias
TABLE
Forward bias
S.No.
V (volts)
I (mA)
1
2
3
4
5
6
Reverse bias S.No.
-V (volts)
-I (µA)
1
3
4
5
6
2
mA Forward bias
RESULT: The Volt – Ampere characteristics of a given PN Junction Diode are studied. PRECAUTIONS 1. See that all the connections given properly 2. Identify the position of the diode, whether it is in forward or reverse bias. 3. Do not apply voltage beyond certain values in either bias.
V
Reverse bias
Figure 9.3
EXPERIMENT NO. 9 B AIM: To study the V-I characteristics of given Zener Diode and to determine Zener break down voltage also find the forward and reverse resistance. APPARATUS:Zener diode (3Z15V), 3 watts, Resistor 75 , 5W, Ammeter (0-500mA), Voltmeter (0-30V), RPS.
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THEORY: Diodes are designed with adequate power supply dissipation capabilities to operate in breakdown voltage region may be employed as voltage reference as without voltage devices. Such diodes are known as avalanche diode. Breakdown or zener diode, two mechanisms of breakdown of diode for increasing reverse voltage are found. First we thermally generated potential to produce new carriers in turn produce additional carrier again through process of miscopying bonds. Even if initially available carriers don’t acquire sufficient energy to disrupt bonds. It is possible to initiate breakdown voltage through a direct rupture of bonds because of existence of strong electric field under these circumstances. Breakdown is known as zener breakdown. PROCEDURE
VS (0-30V) R PS
Forward Bias: To determine forward characteristics built up the circuit as shown in the figure. Increase the source value voltage Vcs so that voltmeter advances in steps of 0.05V. Note the corresponding ammeter reading for increment value of Vf. Reverse Bias: To determine reverse characteristics built up the circuit as shown in the figure. Increase source voltage VBB so that voltmeter reading advances in steps of 0.5 V. Note that corresponding ammeter reading IZ for every increment at value of VZ. Tabulate all readings and plot forward characteristics.
+A _ +
(0-30 mA)
VBB (0-30V) R PS
_
_
+
_
Zener Diode
VF
+
+
75 ohms, 5W
A _
_ +
02
3Z15V
+ _
_ VZ
Figure 9.5: Reverse bias circuit
S.No.
VF (Volt)
IF (mA)
1 2 3 4 5
VZ (Volt)
S.No.
IZ μA
1 2 3 4 5
CALCULATIONS +I(mA)
VF Static forward resistance, R F I F
= ......... IF VZ
VR Static reverse resistance, R R I R
= .........
VF Dynamic forward resistance I F
= .........
VZ Dynamic reverse resistance I Z
-V VsHs
VF Barrier Potential
I Z Mar 22 mA IZ -I(mA)
= .........
Figure 9.6
+V(VsHs)
+
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RESULT Dynamic forward resistance Static forward resistance Dynamic reverse resistance Static reverse resistance
= = = =
PRECAUTIONS 1. 2.
Care must be taken that all the sources and meters are connected with correct polarity. See that the current limit of regulated power supply is set to 250mA.
VIVA-VOCE 1. 2. 3. 4. 5. 6.
What is a Zener diode? What do you understand by breakdown voltage? Explain Zener and Avalanche breakdown? What is knee voltage? Explain the role of doping for different behavior of diodes. Can we interchange the V axis and I axis of diode characteristic curve? If not why?
REFERENCES 1 2 3 4 5 6 7 8
Practical Physics – Gupta.Kumar A text book of Practical Physics – R.K Goel.Govind Ram B.Sc Practical Physics – C.L Arora Electronics fundamentals and applications – Ryder, J.D Properties of silicon and germanium – Conwell,E.M Engineering Physics- M.N Avadhanulu, A.A Dani and P.M Pokley A Laboratory Manual of Physics – D.P Khandelwal B.Sc Practical Physics – Harnam Singh
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EXPERIMENT NO. 10 AIM: Measuring the Diameter of a Human Hair by Laser Diffraction THEORY: Often it is necessary to determine the diameter of a fine wire, thin thread or other object that cannot be measured by convectional means. These items can be measured by using methods of diffraction and interference known as Young’s Double Slit Experiment. While Young’s experiment deal with the pattern of light impinging on two narrows slits separated by a small distance, the method can by applied to an object with a small diameter as well. Where the diameter is within an order of magnitude of the wavelength of laser light used. PROCEDURE 1 Take a 15 cm by 15 cm piece and make a 10 cm by 10 cm hole in the center of the cardboard piece. This is your mounting bracket.
2. 3
4.
Select one strand of hair approximately 15-25 cm long. This hair needs to be mounted on the mounting bracket from step 1. Mount the hair on the bracket using tape. Place the hair so that it bisects the mounting bracket. Make sure the hair is taut and straight.
Set the laser pointer (or laser) on the lab table. Positioning the laser so the beam strikes the hair in the mounting bracket. (You may use binder clips or books to position the laser source and the mounting bracket on the table.)
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7.
8.
9.
10.
38
Make sure the laser setup and mounting bracket face a wall or screen. Record the following key parameters on the data sheet provided. Record the wavelength of the laser as . In some case it may be necessary to average the wavelength values given on the laser’s label. Typical values for a red HeNe Laser are 632-634 nm. Red laser pointers have a typical range between 630 nm –680 nm. Record the distance (D) between the mounting bracket and screen or wall. (If you are using a wall for a screen it might be prudent to tape a piece of white paper on the wall to use as a background.) Examine the pattern striking the screen. It should appear similar to the image below. (You may need to darken the work area or room to see the faint higher order bands.)
Carefully measure the bright bands by measuring from the center of the bright centralband to the starting edge of first bright band on the left. Record this value as y1i, under the ymi column. (You may find a bring spot in the center of the central band. This point can be used as reference.) Measure from the center of the central band again to the end of the first bright band on the left. Record this as y1f, under the ymf column. The average of these two measurements is the distance between the central bright band and the 1st order maximum (m=1) on the left side. Record this on the data table as y1avg under the ymavg column on the data sheet. Repeat the steps for the 2nd, 3rd, 4th and 5th order bands. If you can see the bands beyond m = 5, measure those as well. Make sure you measure from the middle of the central band to the beginning and the end of each of the mthorder bands. (You may have to darken the room to see all the bands.) After measuring all the bands on the left. Proceed to measure the mth order bands on the right side of the central band using the same techniques outlined in step 8. This should yield a total set of at least ten measurements. For each ymavg calculate the diameter of the human hair (d) using:
d m D ymavg 11.
After determining the ten values of d calculate the average diameter of a human hair and the standard error (d ) in the measurement of d. where the standard error is the standard deviation of d divided by the square root of the number of measurements taken.
d Sd N1/2 EXAMPLE CALCULATIONS Example for the 1st order (m = 1) band for a HeNe laser wavelength = 633 nm, and screen distance of D = 1.5 m.
d1 633 109 m 11.5 0.02m 4.75 105 m or 47 m
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Example for the 4th order (m = 4) band for a He Ne laser wavelength = 633 nm, and secreen distance of D = 1.5 m.
d 4 633 109 m 4 1.5 0.0575m 6.61 105 m or 66 m The same experiment can be tried out on a needle or pin.
VIVA-VOCE 1. 2. 3. 4. 5. 6.
What is the range of values for human hair? Average the range of values of human hair. What is the percent difference between your average value and the average accepted value from different sources of information such as books or internet? What other items could you measure using this technique? What is He-Ne laser? How it works? Why we can’t measure human hair diameter using screw gauge? What is diameter of dust particle (floating in air)?
Diamter of a human hair Data Sheet Laser wavelength = Ymi m | m | +7 +6 +5 +4 +3 +2 +1 0 -1 -2 -3 -4 -5 -6 -7
7 6 5 4 3 2 1 N/A 1 2 3 4 5 6 7
Ymf
Ym avg
N/A
Average Diameter Error
Calculated Diameter
N/A
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Some examples of diameter of human hair Bibliographic entry
Result
Standardized Result
"45 microns, 2 times smaller than the diameter of a human hair and close to the limit of resolution for the human eye"
90m
Denny R's Homepage. Denny & Gayle Rossbach. Palmdale, CA
"Diameter of a human hair inches: 0.001; centimeters: 0.00254"
25.4 m
Why Choose A Water Treatment System? Aqua-Fresh Drinking Water Systems, Inc
"Particulate contaminants including asbestos, rust, sediment, dirt, and scale as small as 0.2 microns (1/300th diameter of a human hair)."
Hair - Important Facts About Hair. CAQTI Cosmetics, Inc.
"Flaxen hair is the finest, from 1/1500 to 1/500 of an inch in diameter … and black hair is the coarsest, from 1/450 to 1/140 of an inch."
Piezo Technology. Epson (UK) Ltd.
60 m
17 50 m (flaxen)
51 181 m (black)
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EXPERIMENT NO. 11 AIM: Study of both the current - voltage characteristic and the power curve to find the maximum power point (MPP) and efficiency of a solar cell. APPARATUS: Solar Panel Consist of 6 solar Cells, Table lamp, Digital/Analog D.C ammeter and voltmeter. THEORY: A solar cell or photovoltaic cell is a device that converts light energy into electrical energy. Sometimes the term solar cell is reserved for devices intended specifically to capture energy from sunlight, while the term photovoltaic cell is used when the light source is unspecified. Fundamentally, the device needs to fulfill only two functions: photo generation of charge carriers (electrons and holes) in a light-absorbing material, and separation of the charge carriers to a conductive contact that will transmit the electricity. This conversion is called the photovoltaic effect, and the field of research related to solar cells is known as photovoltaic. Solar cell n
P
2V/20V +
V
10E/Step RL
20/200 mA + mA
Figure 11.1 Sunlight Energy
+
Silicon Coating
P N
Metal Contact Junction Metal Contact
(B) Cross-section
(A) Circuit Symbol
Figure 11.2: Solar cell APPLICATIONS
• Telecommunication systems: Radio transceivers on mountain tops or telephone boxes in the country can often be solar powered. • Remote monitoring and control: scientific research stations, seismic recording, weather stations, etc. use very little power which, in combination with a dependable battery, is provided reliably by a small PV module. • Ocean navigation aids: many lighthouses are powered by solar cells. • Water Pumping/Rural Electrification/Domestic supply • Health Care/Lighting • Electronic industry • Electric Power Generation in Space.
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SIMPLE EXPLANATION 1. 2.
3.
Photons in sunlight hit the solar panel and are absorbed by semiconducting materials, such as silicon. Electrons (negatively charged) are knocked loose from their atoms, allowing them to flow through the material to produce electricity. The complementary positive charges that are also created (like bubbles) are called holes and flow in the direction opposite of the electrons in a silicon solar panel. An array of solar panels converts solar energy into a usable amount of direct current (DC) electricity.
PHOTO GENERATION OF CHARGE CARRIER When a photon hits a piece of silicon, one of three things can happen: 1. The photon can pass straight through the silicon this (generally) happens for lower energy photons, 2. The photon can reflect off the surface, 3. The photon can be absorbed by the silicon which either: Generates heat or Generates electron-hole pairs, if the photon energy is higher than the silicon band gap value. CHARGE CARRIER SEPARATION There are two main modes for charge carrier separation in a solar cell: 1. Drift of carriers, driven by an electrostatic field established across the device 2. Diffusion of carriers from zones of high carrier concentration to zones of low carrier concentration (following a gradient of electrochemical potential). In the widely used p-n junction designed solar cells, the dominant mode of charge carrier separation is by drift. However, in non-p-n junction designed solar cells (typical of the third generation of solar cell research such as dye and polymer thin-film solar cells), a general electrostatic field has been confirmed to be absent, and the dominant mode of separation is via charge carrier diffusion. PROCEDURE Take the Solar Energy Trainer NV6005 along with Solar Panel. Place the solar panel in the stand and adjust the panel at an angle of about 45º with the ground. Direct the sunlight straight at the solar panel (angle of 90º). Note: If sunlight is not properly available then any source of light like lamp can be used. 3. With the DB15 connector connect the Solar Energy Trainer NV6005 with Solar Panel. Then wait for 1 minute to avoid errors due to temperature fluctuations. 4. Set the potentiometer to maximum resistance i.e. at fully clockwise position and measure and record its resistance into the Observation Table. 5. Connect the solar cell as shown in the following circuit diagram as shown in figure 11.3. 1. 2.
a. Connect positive terminal of solar cell to P1 terminal of the potentiometer. b. Connect other end of potentiometer i.e. P2 to positive terminal of ammeter. c. Connect negative terminal of ammeter to negative terminal of solar cell. d. Now connect the positive terminal of voltmeter to P1 and negative terminal of voltmeter to P2. 6.
Record the values of corresponding voltage and current into the observation Table.
+
V
P1
P2
+
Solar Cells Panel
Figure 11.3
A
-
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Now gradually move the potentiometer in anti- clockwise direction so that the resistance of the potentiometer decreases. Now measure the resistances at successively smaller values and record the corresponding values of voltages and current into the Observation Table below. Note: Always to measure the resistance of potentiometer at any position, first remove the patch cords from P1 and P2 and measure resistance by multi meter. Reconnect these connections again for further measurements. 7.
OBSERVATION TABLE
S.No.
Resistance, R
Voltage, V (Volt)
Current, I (mA)
Power Calculated P = V.I (watt)
1 2 3 4 5 6 7 8 8.
Plot the V-I characteristics from the measurements recorded in the table, to show how the photoelectric current depends on the photoelectric voltage and to find maximum power point.
Fillfactor Calculation
ISC
Fill factor is the ratio of maxmium useful power to ideal power: Maximum useful power is area of largest rectangle that can be formed under V-I curve. Vm and Im are values of voltage and current for these conditions.
0.16 0.14 0.12
Ideal power VOC ISC
0.04 0.02
where ISC = maximum value of saturation current VOC = emf genrated by photovoltaic cell in open circuit.
Vm Im VOC ISC
From V-I characteristics you can easily find the maximum power point (MPP). MPP occurs where the product of voltage and current is greatest.
9.
Plot the curve of power as a function of voltage from the measurements recorded in the table.
Expected Power - Voltage curve is as shown in figure 11.6.
Vm 0.5
1 Voltage (V)
1.5
VOC 2.0
ISC
Figure11.4: Current voltage characteristic of the solar cell MPP 0.25 Power (W)
Fill factor
Im
0.10 0.08 0.06
Maximum useful power Vm Im And
MPP
0.2 0.15 0.1 0.05 0.5
1 Voltage (V)
1.5
2.0
Figure 11.6: Power curve of the solar cell as a function of voltage
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The maximum power point (MPP) is the maximum value of power in the above curve. The resistance, RMPP, at which the output power is at a maximum, can be calculated using the following formula:
R MPP
VMPP IMPP
TO CALCULATE THE EFFICIENCY (η) OF SOLAR CELL The efficiency of the solar cell is the ratio of produced electrical power (Pout) and the incident radiant power (Pin).
Pout Efficiency of solar cell, η = P in Where Pout is the output electrical power (maximum power point). Pin is calculated by multiplying approximated irradiance (“irradiance” means radiant power of the light incident per unit area) by the effective area of the solar cell on the panel. This method used the fact that the practical value of the current (maximum photoelectric current measured) is proportional to the photons (radiation) striking the solar cell. This current is therefore proportional to the incident radiant power of the light. The open circuit voltage depends on the semiconductor material of which solar cell is made. It is not proportional to the incident radiant power and therefore cannot be used for this measurement. PROCEDURE 1.
Pout Efficiency of solar cell, η = P in Where Pout (Output Electrical Power) = Maximum Power Point (MPP) Pin (Incident radiant power) = Approximated Irradiance Area of solar cell = (F Ip) A A 2 Here A = Area of a solar cell (Length x Breadth) m Ip= Practical value of current (maximum photoelectric current measured) indicated on the ammeter, F is a constant and is given by
Maximum solar Irradiance Specified by manufactured Maximum value of current The maximum irradiance in summer is approx. 1000 W/m2. The maximum value of the current specified by the manufacturer is achieved at this value i.e. 150mA in the given solar cells. (The parameters of the solar cell/panel are related to the standard test conditions of 1000W/m2 and cell temperature of 25º C.) F=
W m2 F= 150 mA 1000
W m .mA Multiplying the practical value of current (Ip) indicated on the ammeter by the factor gives an approximation of the radiant power per unit area (irradiance) striking the solar cell. 6.67
2.
F 6.67
2
W m -mA 2
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Approximation of the radiant power per unit area =………. Now measure the area in m2 and put the values in the formula given in eq. Pin = ……… Now, we can calculate the efficiency of solar cell with
η=
Pout PIn
Where Pout or MPP =………….. (As calculated before in experiment) η =……….. The efficiencies of solar cells lie between 12 to 15 %. If efficiency is slightly less than determined value then it is due to measuring errors and inaccuracies in determining the incident radiant power. Furthermore, the efficiency of solar panel is less than that of their separate constituent cells. This is caused by losses that arise in matching solar cells that do not
all have exactly the same properties. If the solar cells are connected in series to generate desired voltage, the maximum power point may not be same for all cells. Solar cell losses arise as not all photons striking the solar cell can be converted into charge carriers. Part of the light is reflected as soon as it hits the surface and the metal contacts cast shadows. Since the photon energy does not correspond to the energy gap, less than half of the incident energy is used. Recombination of charge carriers (atomic rebinding of electrons) and electrical losses caused by internal resistances (ohmic losses in the semiconductor) of the solar cell and its contacts also arise. PRECAUTIONS 1. 2. 3.
Do not make inter connections on the board with mains switched ON. All the connections should be tight. Switch off after taking the readings.
VIVA-VOCE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
What is solar cell? Why solar cell is also called photovoltaic cell? What are the uses of solar cell? What do you mean photoelectric effect? On what factors does the photocurrent depend? Define the efficiency of Solar Cell? How does temperature effect efficiency of solar cell/photo voltaic cell. What happens to the current when Photo voltaic cells are connected in series and in parallel. What is the order of current in photo voltaic cell? Define a fill factor of a photo voltaic cell.
REFERENCES 1 2 3 4 5 6 7 8
Practical Physics – Gupta.Kumar A text book of Practical Physics – R.K Goel.Govind Ram B.Sc Practical Physics – C.L Arora Electronics fundamentals and applications – Ryder, J.D Properties of silicon and germanium – Conwell,E.M Engineering Physics- M.N Avadhanulu, A.A Dani and P.M Pokley A Laboratory Manual of Physics – D.P Khandelwal B.Sc Practical Physics – Harnam Singh
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EXPERIMENT NO. 12 AIM: To determine the wavelength of sodium light (Monochromatic source) with the help of Fresnel’s Bi- Prism. APPARATUS: Optical bench with uprights, sodium lamp, Bi-prism, convex lens, slit and micrometer eyepiece. Slit and micrometer eye piece are already fitted on the optical bench. FORMULA The wavelength l of the sodium light is given by the formula in the case of Bi-prism experiment. Where b 2d D Again Where d1 d2
= fringe width, = distance between the two virtual sources, = distance between the slit and screen (Eye piece upright). 2d
d1d 2
= =
distance between the two images formed by the convex lens in one position. distance between the two images formed by the convex lens in the second position.
APPLICATIONS • To make two coherent source for interference .Bi prism make two sources. • To find wavelength of a monochromatic light source and for determining the thickness of a thin glass sheet when placed between bi prism and screen or eyepiece. DESCRIPTION OF THE APPARATUS
Slit
Biprism
Lens
Eye Piece
Source of Light
Two coherent sources, from a single source, to produce interference pattern are obtained with the help of a Bi-prism. A Bi-prism may be regarded as made up of two prisms of very small refracting Figure 12.1 angles placed base to base. In actual practice a single glass plate is suitably grinded and polished to give a single prism of obtuse angle 1790 leaving remaining two acute angles of 30¢ each The optical bench used in the experiment consists of a heavy cast iron base supported on four leveling screws. There is a graduated scale along its one arm. The bench is provided with four uprights which can be clamped anywhere and the position can be read by means of vernier attached to it. Each of the upright is subjected to the following motions: (i) motion along bench, (ii) transverse motion (motion right angle to bench), (iii) rotation about the axis of the upright, (iv) with the help of a tangent screw, the slit and Bi-prism can be rotated in their own vertical planes. The bench arrangement is shown in figure 12.1 P
ACTION OF BI-PRISM The action of the Bi-prism is shown in figure 12.2. Monochromatic light from a source S falls on two points of the prism and is bent towards the base. Due to the division of wave front, the refracted light appears to come
d
S1
E
S
C
S2
F y1
y2
Figure 12.2
Q
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from S1 and S2. The waves from two sources unite and give interference pattern. The fringes are hyperbolic, but due to high eccentricity they appear to be straight lines in the focal plane of eyepiece. PROCEDURE ADJUSTMENTS 1. Level the bed of optical bench with the help of spirit level and leveling screws. 2. The slit, Bi-prism and eye piece are adjusted at the same height. The slit and the cross wire of eye piece are made vertical. 3. The micrometer eye piece is focussed on crosswire. 4. With an opening provided to the cover of the monochromatic source, the light is allowed to incident on the slit and the bench is so adjusted that light comes straight along its lengths. This adjustment is made to avoid the loss of light intensity for the interference pattern. 5. Place the Bi-prism upright near the slit and move the eye piece sideway. See the two images of the slit through Bi-prism; if they are not seen, move the upright of Bi-prism right angle to the bench till they are obtained. Make the two images parallel by rotating Bi-prism in its own plane. 6. Bring the eyepiece near to the Bi-prism and give it a rotation at right angle of the bench to obtain a patch of light. As a matter of fact, the interference fringes are obtained in this patch provided that the edge of the prism is parallel to the slit. 7. To make the edge of the Bi-prism parallel to the slit, the Bi-prism is rotated with the help of tangent screw till a clear S1 interference pattern is obtained. These fringes can be easily seen even with the S S2 naked eye. Slit
Lateral Shift The line joining the centre of the slit and the edge of the Bi-prism should be parallel to the bed of the bench. If this is not so, S1 there will be a lateral shift and the removal is most important. This is shown in S S2 figure 12.3. (a) In order to adjust the system for No Lateral Shift no lateral shift, the eyepiece is Figure 12.3 moved away from Bi-prism. In this case, the fringes will move to the right or left but with the help of base screw provided with Bi-prism, it is moved at right angle to the bench in a direction to bring the fringes back to their original position. (b) Now move the eyepiece towards the Bi-prism and the same adjustment is made with the help of eyepiece. Now using the process again and again, the lateral shift is removed.
MESUREMENTS: (A) 1. 2. 3.
MEASUREMENT OF FRINGE WIDTH (b) Find out the least count of the micrometer screw. Place the micrometer screw at such a distance where fringes are distinct, bright and widely spaced, (say 100 cm.) The crosswire is moved on one side of the fringes to avoi8d backlash error. Now the cross wire is fixed at the centre of a bright fringe and its reading is noted on the main scale as well as on micrometer screw.
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4.
The crosswire is now moved and fixed at the centre of every second bright fringe. The micrometer readings are noted. From these observations b can be calculated.
(B)
MEASUREMENT OF D : The distance between slit and eyepiece uprights is noted. This distance gives D. The value of D is corrected for the bench error.
(C)
MEASUREMENT OF 2d:
The distance 2d between the two virtual sources can be measured with the help of fig.(4). 1. To obtain the value of 2d, the positions of slit and Bi-prism uprights are not disturbed. 2.
A convex lens is introduced between Bi-prism and eye-piece and moved in between to obtain two sharp and focused images of the source. The distance between two images is noted. In the first position figure 12.4 the distance is denoted by d1.
3.
The lens is again moved towards eyepiece to obtain the second position where again two sharp and focused images are obtained. The distance in this case is denoted by d2. Knowing d1 and d2. Knowing d1 and d2, 2d can be calculated by using the formula 2d
d1d 2
S1 d2
2d
d1
1st position of lens 2nd position of lens
S2
Figure 12.4 OBSERVATIONS Pitch of the screw No. of divisions on the micrometer screw L.C.of micrometer screw
= …. cm. = …. cm. = ….. cm.
(I)TABLE FOR FRINGE WIDTH b : No. of frings
Micrometer reading (a) No. of Micrometer reading (b) Deifference Mean frings for 10 for 10 Total Total V.C. V.C. M.S. M.S. fringes frings cms. reading reading cms. reading reading (a b) cms cms
1
......
......
......
11
......
......
......
......
3
......
......
......
13
......
......
......
......
5
......
......
......
15
......
......
......
......
7
......
......
......
17
......
......
......
......
9
......
......
......
19
......
......
......
......
......
Fringe width β cms.
......
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MEASUREMENT OF 2d: Position of upright carrying list Position of upright carrying the eyepiece Observed value of D
= ….. cm. = ….. cm. = ….. cm.
MEASUREMENT OF 2d: S.No.
Micrometer reading 2nd position of lens
1st position of lens I image a
II image b
d1 = b a I image a
II image b
2d =
d1d2
Mean 2d
d2 = b a
1 2 3 CALCULATIONS λ β
2d D
..........Ao
RESULT: Wavelength of sodium light Standard value of Percentage error
= … A0 = … A0
Standard value - Experimental value 100 Standard value
= .......%
PRECAUTIONS 1. 2. 3. 4. 5. 6. 7. 8.
The setting of the uprights at the same level is essential. The slit should be vertical and narrow. Fringe shift should be removed. Bench error should be taken into account. Crosswire should be fixed in the centre of the fringe while taking observations for fringe width. The micrometer screw should be rotated only in one direction to avoid backlash error. The fringe width should be measured at a fairly large distance. Convex lens of shorter focal length should be used (f = 25 cm. approx.).
THEORETICAL ERROR We know
λ β
2d β D
d1d 2 D
Taking loge and differentiating, we get , In our case,
d1 d 2 .....
D 1 d1 1 d 2 D 2 d1 2 d 2
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VIVA-VOCE 1. 2. 3. 4. 5. 6. 7. 8.
What do you mean by monochromatic light? What is Bi-prism? What is the function of Bi-prism in this experiment? What are coherent sources? Is it possible to observe interference fringes with light coming from two independent lamps or candles? What do you mean by interference of light? How many types of interferences have you read? What are the conditions for obtaining well defined and distinct interference? Is there any loss of energy in interference? What is fringe width? Are the fringes equally spaced? Are the Biprism fringes perfectly straight?
REFERENCES 1 2 3 4 5 6 7 8
Practical Physics – Gupta.Kumar A text book of Practical Physics – R.K Goel.Govind Ram B.Sc Practical Physics – C.L Arora Electronics fundamentals and applications – Ryder, J.D Properties of silicon and germanium – Conwell,E.M Engineering Physics- M.N Avadhanulu, A.A Dani and P.M Pokley A Laboratory Manual of Physics – D.P Khandelwal B.Sc Practical Physics – Harnam Singh
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EXPERIMENT NO. 13 AIM: To determine the dispersive power of a material of prism using Spectrometer. APPARATUS: Spectrometer, Prism, Mercury Vapor Lamp. THEORY: A spectrometer is used to measure the necessary angles. The spectrometer consists of three units: (1) collimator, (2) telescope, and (3) prism table. The prism table, its base and telescope can be independently moved around their common vertical axis. A circular angular scale enables one to read angular displacements (together with two verniers located diametrically opposite to each other). In the experiment, we need to produce a parallel beam of rays to be incident on the prism. This is done with the help of a collimator. The collimator has an adjustable rectangular slit at one end and a convex lens at the other end. When the illuminated slit is located at the focus of the lens (See Fig. 1), a parallel beam of rays emerges from the collimator. We can test this point, with the help of a telescope adjusted to receive parallel rays. We first prepare the telescope towards this purpose as follows: SETTING THE EYEPIECE: Focus the eyepiece of the telescope on its cross wires (for viewing the cross wires against a white background such as a wall) such that a distinct image of the crosswire is seen by you. In this context, remember that the human eye has an average “least distance of distinct vision” of about 25 cm. When you have completed the above eyepiece adjustment, you have apparently got the image of the crosswire located at a distance comfortable for your eyes. Henceforth do not disturb the eyepiece. SETTING THE TELESCOPE: Focus the telescope onto a distant (infinity!) object. Focusing is done by changing the separation between the objective and the eyepiece of the telescope. Test for the absence of a parallax between the image of the distant object and the vertical crosswire. Parallax effect (i.e. separation of two things when you move your head across horizontally) exits, if the cross-wire and the image of the distant object are not at the same distance from your eyes. Now the telescope is adjusted for receiving parallel rays. Henceforth do not disturb the telescope focusing adjustment. SETTING THE COLLIMATOR: Use the telescope for viewing the illuminated slit through the collimator and adjust the collimator (changing the separation between its lens and slit) till the image of the slit is brought to the plane of crosswires as judged by the absence of parallax between the image of the slit and cross wires. OPTICAL LEVELING OF THE PRISM: The prism table would have been nearly leveled before use has started the experiment. However, for your experiment, you need to do a bit of leveling using reflected rays. For this purpose, place the table with one apex at the center and facing the collimator, with the ground (non-transparent) face perpendicular to the collimator axis and away from collimator. Slightly adjust the prism so that the beam of light from the collimator falls on the two reflecting faces symmetrically (Fig. 2) when you have achieved this lock the prism table in this position. Turn the telescope to one side so as to receive the reflected image of the slit centrally into the field of view. This may be achieved by using one of the leveling screws. The image must be central whichever face is used as the reflecting face. Similarly, repeat this procedure for the other side.
Figure13.1: Experimental setup angle of prism
FINDING THE ANGLE OF THE PRISM (A): With the slit width narrowed down sufficiently and prism table leveled, lock the prism table and note the angular position of the telescope when one of the reflected images
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coincides with the cross wires. Repeat this for the reflected image on the other side (without disturbing the prism and prism table). The difference in these two angular positions gives 2a. FINDING ANGLE OF MINIMUM DEVIATION (DM) Unlock the prism table for the measurement of the angle of minimum deviation (Dm). Locate the image of the slit after refraction through the prism as shown in Fig. 3. Keeping the image always in the field of view, rotate the prism table till the position where the deviation of the image of the slit is smallest. At this position, the image will go backward, even when you keep rotating the prism table in the same direction. Lock both the telescope and the prism table and to use the fine adjustment screw for finer settings. Note the angular position of the prism. In this position the prism is set for minimum deviation. Without disturbing the prism table, remove the prism and turn the telescope (now unlock it) towards the direct rays from the collimator. Note the scale reading of this position. The angle of the minimum angular deviation, viz, Dm is the difference between the readings for these last two settings. PRINCIPLE: Refractive Index (µ): It is defined as
µ =
And
velocity of light in vaccum velocity of light in air
A Dm sin sin i 2 A sin r sin 2
Where A Angle of Prism Dm Angle of minimum deviation OBSERVATION TABLES For angle of the prism: Vernier
Telescope reading for reflection from first face
Telescope reading for reflection from second face
M
V
Total (a) M
V
S
S
S
S
R
R
R
R
Difference (a~b) = 2A
Mean A value of 2A
Mean A (Degrees)
Total (b)
V1 V2
PROFESSIONAL’S Physics Lab Manual - I
53
2. For angle of minimum deviation: S.
Colour
Vernier
No
V1
1.
green
Dispersed image telescope in minimum deviation position
Telescope reading for direct image
M
V
Total
M
V
S
S
(a)
S
S
R
R
R
R
Difference
Mean deviation Dm (Degrees)
(a ~ b) Total (b)
V2
V1
2.
blue
V2
DISPERSIVE POWER ( w ):- Angular rotation for a given wavelength is called dispersive power of the material of a prism
READINGS Direct ray reading
= R
Green colour reading
=R1
Blue colour reading
= R2
Minimum deviation angle for green Dg = R R1 Minimum deviation angle for blue Db = R R2 A DB sin 2 b A sin 2
A Dg sin 2 , G A sin 2
Dispersive power of the material of the prism , Where SPEED OF LIGHT IN PRISM: Speed of light in prism is given by
PROFESSIONAL’S Physics Lab Manual - I
54
PRECAUTIONS 1. 2.
Take the readings without any parallax errors The focus should be at the edge of green and blue rays
RESULTS: The dispersive power of a material of given prism using spectrometer is ω = Speed of light in prism υ =
VIVA-VOCE 1.
What do you mean by dispersive power? Define it.
2.
On what factors, the dispersive power depends?
3.
What is a normal spectrum?
4.
Can you find out the dispersive power of a Prism with sodium light?
5.
How many types of spectra you know? What type of spectra do you expect to get from (i) an incandescent filament lamp (ii) sunlight (iii) mercury lamp?
6.
What is the difference between a Telescope and a Microscope?
REFERENCES 1
Practical Physics – Gupta.Kumar
2
A text book of Practical Physics – R.K Goel.Govind Ram
3
B.Sc Practical Physics – C.L Arora
4
Electronics fundamentals and applications – Ryder, J.D
5
Properties of silicon and germanium – Conwell,E.M
6
Engineering Physics- M.N Avadhanulu, A.A Dani and P.M Pokley
7
A Laboratory Manual of Physics – D.P Khandelwal
8
B.Sc Practical Physics – Harnam Singh
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