Content 1

 

CONTENTS   Sl. No 

Item 

1. 

Objective 

2. 

Introduction 

3. 

Apparatus 

4. 

Theory 

5. 

Procedure 

6. 

Observations 

7. 

Diagrams 

8. 

Calculations + Graphs 

9. 

Precautions 

10. 

Bibliography 

Page No. 

 

OBJECTIVES:  

 To study the variation of the angle of deviation   with the angle of  

incidence using  Hollow Glass Prism and to determine the angle of minimum deviation. 

 To find out the refractive index   of   various liquids using a Hollow  

Prism. 

INTRODUCTION:  

This  project is of Investigatory Type. In this project, a hollow prism has been used to calculate calculate the re refractive fractive index of various liquids. The hollow  prism is filled with with liquid and then the experiment is pe performed. rformed. 

 

APPARATUS:  

rawing Board 

eet of Paper  

ollow Glass Prism 

raph Paper  

rotractor  

rawing Pins 

ll Pins 

encil 

THEORY:   

Reff r acti Re action on :    In a homogenous medium, light travels along a straight line,but whenever it falls on a surface of another medium, a very small fraction of it is reflected back and most of the light passes into the medium, though with a change change of direction. This phenomenon of the bending of light at the surface of separation of the two medium is called refraction of light. 

 

Cause Caus es of r ef r acti acti on :   This phenomenon of refraction takes place when a beam of light enters a medium in which light enters a medium in which light travels with a different velocity. 

L aws Of Ref Ref r acti action:  on:    1.  The incident ray, the refracted and the normal to the surface at the point of incidence lie on the same plane.  2.  For any two given media, the ratio of the sine of the angle of incidence to the angle of refraction is a constant, where it is the angle of incidence and is the angle of refraction.  

Medium: The surrounding substance through which the light travels.   For a monochromatic light, the ratio of the sine of the angle of incidence to the sine of angle of refraction is a constant for any two given media. If `I’ is the angle of incidence, and `r’ is the angle of refraction, then;  Sine( I)  ------Sine( R) 

=

Constant 

the constant is called the refractive index. For most purposes it may be assumed that the refractive index is with respect to air.  

 

 

When light travels from a rarer to a denser medium, it bends

towards the normal and vice versa when it goes from a denser to a rarer medium. It has been experimentally shown that 

Refractive index of substance =

Velocity of light in air  ----------------------------------------- -----------------------------   Velocity of light in substance 

  Reff r ac Re action tion T Thr hr oug ough h Pr i sm: 

A transparent medium bounded by two plane surface inclined to each other at an angle is called called a Prism Prism.. The angle betw between een the two faces is known as the angle of the prism.  

[C1]  A ngl e of de deviati viati on  :  :    The angle through which the inci incident dent ray of light is deviated is called the angle of deviation. In fact it is the the angle  between the emergent emergent ray and the incident incident ray produced. 

Angle An gle of mi ni mum dev devi ation  :  :   As the value value of the angle of incidence incidence (1) increases, the angle of deviation decreases till for a particular value of the angle of incidence, it attains a minimum value m , is called the angle of minimum deviation. 

 

 :   Cri tical tical angle  angle 

It is that angle of incidence in the denser medium for which corresponding angle of refraction in the rarer medium is 90 degree.   I  = ---------   Sin C 

Where,  - Refractive Index  C  -

Critical angle 

The four parameters on which angle of deviation depends are:  1.  Angle of prism

( A ) 

2.  Material of prism (

) 

3.  Angle of incidence ( I )  4.  Wavelength or color of light (   ) 

 

Reff r action Re action thr thr ough Pri sm :    Th eory on on r ef r acti acti on thr ough P Prr i sm :    When a ray of light passes from one   medium into the other, it either bends towards the normal or away from the normal in the second medium, depending upon whether the second medium is denser or rarer with respect to first medium. This phenomenon is know known n as as the Refr Re fr ac action tion of li ght. 

For a particular particular pair of two media, and for a particular wavelength wavelength of light (colour) the ratio of the sine of the angle of incidence and the sine of the angle of refraction is a constant quantity called the Refractive Index of the second second medium with respect tto o the first me medium. dium. It is represented by: 

=

Sin i  --------  Sin r 

Therefore , the value of the angle of incidence i can be obtained in terms of the refracting angle A of the prism and the angle of minimum deviation m and the angle of refraction r can also be obtained obtained in terms terms of the refracting angle A of the prism.   Let ABC represent a section of the glass prism and let IP be a ray incident at angle i on the first face AB of the prism at a point P. N1PN

 

is the normal to this face. face. The material of the prism is denser wit with h respect to air, as such the ray will refract in the direction PQ making an angle r 1 with the normal reaching the second fac facee AC of tthe he prism at the point Q making an angle r    with the normal N QT. The ray 2

2

emerging in the direction QE bending away from the normal and making an angle angle e with the the normal. normal.  If the incident ray IP be produced produ ced backwards to meet QE produced at S, the angle KSQ is called the angle of deviation is represented by D. Angle BAC is called the refracting angle of the prism and represented by A.  To derive the relation:  A + D = i + e 

In

 

SPQ, 

PS is produced to K.   KSQ

or D is the external angle.  

D =  SPQ + = i-r 1 + e-r 2 

 SQP 

= (i + e) - (r 1 + r 2) .............(1) .............(1)  r 1 + r  2  2 +  PTQ = 180 0

r 1 + r 2 = 180   -

0

 

 PTQ

.........(2) 

 

Taking quadrilateral APTQ   APT

0

0

+  AQT = 90   + 90  = 180

 A

+  PTQ = 180

 A

= 180 -  PTQ

0

 

0

 

----------------(3) ----------------( 3) 

From (2) and (3)  r 1 + r 2  =

 A.......... A...........(4) .(4) 

From (1) and (4)   D A

= i + e -  A + D =

i + e 

When the angle of deviation D has minimum value D m the following conditions are fulfilled:  i = e and

r 1 - r 2 = r (say) 

Applying these conditions in Eq.(2) and (3)  A = 2 r  

or and Or

A  r = ----2  A + D m  = 2 i  A+Dm  i = --------2 

...........(5) ...........(5) 

............(6) ............(6) 

 

  Sin i  Since u2 = --------  Sin r   We obtain on substituting the value of (i) and (r) ( r) 

since

Sin(i)  = ------------   Sin (r) 

Sin(A+Dm)/2  = ---------------------------------------------- - .........(7)  Sin(A/2) 

Thus we find that we can use the relation (7) for determining the refractive index. The experiment thus consists of finding of the value of the refracting angle of minimum deviation Dm.  For finding the value of Dm a curve is plotted between the angles of incidence(1) and their respective angles of deviation (D). 

 

PROCEDURE:   

1.

Fix the sheet of white paper on Drawing board with cello tape or

2.

drawing pins.  Draw a straight-line XY nearly at the center of the sheet parallel to its length. Mark points marked as as O at suitable spacing on the line X XY Y and draw normal to the line XY at point O. Draw straight line PQ corresponding to the incident rays that are drawn at the angles of incidence ranging from 30 to 60 i.e. for angles 35,40,45,50,55 & 60 using a protractor. 

3.

Fill the liquid from open and of prism. 

4.

Fix two pins P and Q about 8 cm on the incident rayline and view its image with one eye closed from the side of BC of the prism. Fix two  pins R and S on the paper such that the tips of these pins and the tips of these images of the incident ray pins, all lie on the same straight line.  

5.

Join the points (i.e. pin pricks) S & R and produce it backwards to meet the incident ray PQ produced. produced.

Thus RS is the eme emergent rgent ray

corresponding to the incident ray PQ. PQ. Draw arrow heads heads to show the direction of rays.  6.

Measure the angle of deviation D with Protractor. 

7.

Repeat at steps (4 to 8) for different liquids having different values of angle of incidence and measure the corresponding angles of deviation 0

0

D. Take at at least three values values (i) from 30  to 40 .

 

8.

Now place the prism on separate sheet of paper or on the same sheet at a suitable place and trace its triangular boundary with a sharp pencil. Measure the angle A, of the triangle so traced with the help of protractor.  

 

9.

Record your observation in observation table. Plotting Plotti ng of gr aph b be etwe twee en i & D.  

Plot a graph between angle i and D for various sets of values recorded in the observation table.  

 

Precautions

1. 2.

A sharp pencil should be used for drawing the boundary of the prism.   The separation between the pins should not be less than 8 cm.  3.

4.

The angle of incidence should lie between 30-45.  

The same and prism should be used for all observations. So an ink mark should be plac placed ed on it to distinguish it as a refracting angle A of the prism. 

5.

The pins should have sharp tips and fixed vertically and the pin pricks should be encircled immediately after they are removed.  

6.

Proper arrow should be drawn to indicate the incident, the refracted and the emergent rays. 

7. 

A smooth curve passing practically through all the plotted points should be drawn. 

 

 OBSERVATIONS  1) 

FOR H2O: 

Sl.No. 

ANGLE OF

ANGLE OF

INCIDENCE 

DEVIATION 

o

25  

o

24  

o

23  

o

25  

o

26  

1.

35  

2.

40  

3.

45  

4.

50  

5.

55  

o

o

o

o

o

 

1) 

FOR SPIRIT: 

Sl.No. 

1) 

ANGLE OF

ANGLE OF

INCIDENCE 

DEVIATION 

1.

35o 

29o 

2.

40  

3.

45  

4.

50  

5.

Sl.No. 

o

26  

o

o

25  

o

27  

55  

o

28  

ANGLE OF

ANGLE OF

INCIDENCE 

DEVIATION 

o

o

o

For Glycerin: 

4.

FOR BENZENE: 

o

39  

o

38  

o

35  

o

40  

o

41  

1.

35  

2.

40  

3.

45  

4.

50  

5.

55  

o

o

o

 o

o

 

Sl.No. 

ANGLE OF

ANGLE OF

INCIDENCE 

DEVIATION 

o

40  

o

39  

o

41  

o

42  

o

45  

1.

35  

2.

40  

3.

45  

4.

50  

5.

55  

CALCULATIONS

 

Formula Applied:-  Sin (A+Dm )  2      =  -----------------------    Sin (A/2) 

o

o

o

 o

o

 

1. 

Water    Sin (60+23 )  2   =  -----------------------

=

Sin(41.5)   

------------------- 

Sin 30 

Sin(60/2)

=

0.6626

= 1.33 

0.5 

2. 

  Spirit 

Sin (60+25 ) 

  

2 =  -----------------------

Sin(60/2)

=

3. 

Sin 30 

0.6756

= 1.35  0.5000 

Glycerin   

 )  Sin  (60+35     =

2

=

Sin(47.5) 

=

Sin(42.5)  -------------------

 

 

 

--------------------- ----

Sin 30 

Sin(60/2)

=

-------------------

0.7372 --------- 

=

 

1.47  0.5 

4. 

Benzene   

Sin (60+39 )     = 

2

-----------------------

Sin(60/2) =

1.52 

Sin 30 

=

Sin(49.5) 

-------------------

 

 

RESULT  (i) 

The angle of deviation deviation D first decrea decrease se with the increase increase in the angle op-of incidence, attains a minimum value and then increase with further increase in angle of incidence. 

(ii)

The refractive index of :- 

 

i.

Water

= 1.33 

ii.

Spirit

= 1.35 

iii.

Glycerine = 1.47

iv

Benzene

= 1.52