Physics Investigation

Advanced Higher Physics Investigation Interference of Light

By Richard Donaldson Dunfermline High School 063280070

0|Page Richard Donaldson – Advanced Higher Physics

Table of Contents Summary ................................................................................................................................................ 2 Underlying Physics ............................................................................................................................. 2 Interference of light....................................................................................................................... 2 Determination of the wavelength of sodium light using newton’s rings ................................... 3 Track spacing of a CD ..................................................................................................................... 4 Diameter of a human hair .............................................................................................................. 5 Experiment 1: ......................................................................................................................................... 6 Aim: ..................................................................................................................................................... 6 Method: .............................................................................................................................................. 6 Results: ............................................................................................................................................... 7 Calculations ........................................................................................................................................ 7 Calculations of Uncertainties ............................................................................................................ 8 Experiment 2: ......................................................................................................................................... 9 Aim: ..................................................................................................................................................... 9 Method: .............................................................................................................................................. 9 Results ................................................................................................................................................ 9 Calculations ...................................................................................................................................... 10 Calculation of Uncertainties ............................................................................................................ 10 Experiment 3: ....................................................................................................................................... 11 Aim: .................................................................................................................................................... 11 Method: ............................................................................................................................................. 11 Results ............................................................................................................................................... 11 Calculations ....................................................................................................................................... 11 Calculations of uncertainties ............................................................................................................ 12 Investigation Conclusion & Evaluation ............................................................................................... 13 Conclusion: ........................................................................................................................................13 Discussion and Evaluation: ...............................................................................................................13 References ............................................................................................................................................ 15

1|Page Richard Donaldson – Advanced Higher Physics

Introduction Summary In my investigation I used the interference of light to calculate three different lengths. In my first experiment I calculated the wavelength of sodium light. In my second experiment I calculated the track spacing found on a CD using the diffraction of light with a laser, and in my third experiment I calculated the diameter of a human hair using the diffraction of light with a laser. My results from these experiments are as follows: Wavelength of Sodium light Diameter of human hair Track spacing of a CD:

( m

Underlying Physics Interference of light The interference of light is a phenomenon in which either two waves from a monochromatic light source or from more than one coherent light source superimpose to form a wave that results in either constructive or destructive Interference, depending on the phase of the waves in relation to one another. If the two waves meet in phase, then it will result in constructive interference. If the two waves meet 180˚ or 2π radians out of phase, then it will result in destructive interference. This phenomenon has been used to show that light can be seen as both a particle and a wave, but it can also be used to find out variables, such as wavelength, which I will be attempting to find in my experiments.

2|Page Richard Donaldson – Advanced Higher Physics

Determination of the wavelength of sodium light using newton’s rings In 1717, Sir Isaac Newton conducted an experiment in which an interference pattern is created when a convex lens is placed upon a flat glass plate. When viewed with a monochromatic light source, in the case of my experiment; sodium, the pattern known as “Newton’s rings” appears as a concentric pattern of alternating bright and dark rings with a central ring located at the point of contact between the lens and the flat glass plate. The bright fringes are caused by constructive interference and the dark fringes are caused by destructive interference. 1

Let t represent the thickness of the air film at B (t = BD = AF) and let D represent the diameter of the fringe (D = BC = ED). If the radius of the curvature of the curved surface is R, then from the laws of circles we know that:

( )

For B and C to be on a dark fringe, the path difference must equal an integral number of wavelengths to allow the change of phase to be reflected at B, so: (

)

To avoid errors due to the uncertainty of locating the central ring, the diameters of the n th and (n+m)th dark fringes are measured:

Where:     

1

λ is the wavelength D2(n+m) is the diameter of the (n+m)th ring squared D2n is the diameter of the nth ring squared m is a positive integral number R is the radius of the convex lens

Tyler, F. (1971). A Laboratory Manual of Physics SI Units page 74

3|Page Richard Donaldson – Advanced Higher Physics

Track spacing of a CD When a laser is reflected upon a CD, a diffraction pattern is created. If the wavelength of the laser is known, the track spacing of the CD can be calculated. Using the equation nλ=dsinθ 2

Consider the rays which move in a direction with angle θ with the normal to the grating. If the path difference is a whole number of wavelengths, then the waves will meet in phase.

C B Incoming laser light θ

A

This occurs if |CB| = nλ. Sin = O/A Sinθ =

| |

| |

therefore |CB| = CA sinθ. As |CA| is the line spacing of the grating, it

becomes dsinθ, so for a bright fringe, the equation is nλ = dsinθ. Where:  n is the nth order of maximum  λ is the wavelength  Sinθ is the angle  D is the fringe width

The wavelength of the green laser I am using is 532nm, which will stay constant throughout this experiment. Theta can be worked out using trigonometry. The adjacent side can be found by measuring the distance from the CD to the white screen where the interference pattern is shown. The opposite side can be found by measuring the distance from the central order to the first order maximum.

2

Express, S. (n.d.). Proof of nλ = dsinθ.

4|Page Richard Donaldson – Advanced Higher Physics

Diameter of a human hair Often it is necessary to determine the diameter of a fine wire, or another object that for practical reasons, cannot be measured using conventional methods. The diameters of these items, such as a length of human hair, can be measured using methods of light interference and diffraction known as “Young’s Double Slit” Experiment. This experiment was conducted by Thomas Young in 1801 as evidence to support the idea that light can be seen as a wave. A coherent light source is passed through two parallel slits, which is then observed on a screen behind the plates. As the light passes through the slits, the waves interfere with one another, producing bright and dark fringes on the screen.

P

A

Laser

Diffraction bands from edge A Interference fringes

B L

Q

Diffraction bands from edge B

D

3

PQ is the geographical shadow of the hair AB. The effects observed outside P and Q are due to diffraction effects at the edges A and B respectively. The bands between P and Q are due to interference between wavelets which originate at A and B. A and B act as a pair of Young’s slits to give interference fringes between P and Q. now from the theory of Young’s experiment. The fringe width (ω) is given by Dλ/d where D is as given, d is the diameter of the wire and λ is the wavelength of the light used. Hence the diameter d of the wire =Dλ/ω

3

Tyler, F. (1971). A Laboratory Manual of Physics SI Units page 67

5|Page Richard Donaldson – Advanced Higher Physics

Procedures Experiment 1: Determination of the wavelength of sodium light using Newton’s rings

Aim: to determine the wavelength of a sodium light source using the Newton’s rings experiment

Method: Microscope

Convex Lens

Monochromatic

Thin glass plate

4

Light source (Sodium)

Plano-convex Lens

Incident ray Reflected ray

Glass plate

Figure 1 Set up the equipment as shown in the diagrams. Make sure that both of the convex lenses used are thoroughly cleaned. The light is then directed onto the plate glass and convex lens by the thin glass plate at an angle of 45 degrees to the horizontal, adjust the focus on the lens of the microscope until the fringes are sharply in focus. The definition of the fringes can be increased by slightly adjusting the position of the reflecting plate and the sodium vapour lamp. Centre the cross wires on the centre of the central ring within the interference pattern. Move the microscope across the lens and take the readings of diameters of each of the rings, moving in one direction only to avoid backlash.

4

Tyler, F. (1971). A Laboratory Manual of Physics SI Units page 74

6|Page Richard Donaldson – Advanced Higher Physics

Results: No. of fringe

D2(n+m)- D2n

Diameter(m) 3.40E-04 1.16E-03 1.69E-03 2.06E-03 2.37E-03 2.69E-03 2.96E-03 3.15E-03 7.12E-06

Radius of lens Integer

0.3m 10

n(central ring) n+2 n+4 n+6 n+8 n+10 n+12 n+14

Wavelength

Diameter2 (m) 1.16E-07 1.35E-06 2.86E-06 4.24E-06 5.62E-06 7.24E-06 8.76E-06 9.92E-06

592nm

Calculations

D210 – D20 =

 

m = 10 R = 0.3m

Where:     

λ is the wavelength D2(n+m) is the diameter of the (n+m)th ring squared D2n is the diameter of the nth ring squared m is a positive integral number R is the radius of the convex lens

7|Page Richard Donaldson – Advanced Higher Physics

Calculations of Uncertainties Microscope Scale reading in microscope  Main Scale: 0.005mm  Vernier: 0.02mm Total scale reading: 0.025mm Calibration in microscope: 0.01mm Total uncertainty √

√

= 0.02mm

Lenses Calibration: 0.01cm Scale reading: 0.01cm Total uncertainty √

√

= 0.01cm

Error bars were not plotted on the graph due to the uncertainty’s in the diameter of the rings and the radius of the lens being too small to be accurately plotted

Wavelength Using the linest function I was able to calculate the overall uncertainty of the wavelength. By plotting diameter2 against the fringes, I calculated that the uncertainty was:

Therefore the value of the wavelength of sodium light is:

8|Page Richard Donaldson – Advanced Higher Physics

Experiment 2:

Distance to first order

Track spacing of a CD Fringe pattern

Aim: to calculate the track spacing of a CD using diffraction Method:

Distance to screen (d)

d 5

CD

Laser Screen CD

Central area

Set up the experiments as shown in the diagrams. Measure and record the distance from the CD to the screen. Make sure that the laser is positioned at about centre of the CD, as shown in diagram 3. When the laser is turned on, an interference pattern will be present on the white screen. Record the distance between the central order and the first order maximum.

Results O(m) 0.36

A(m) 1.10

Θ(deg) 18.1

0.37 1.10 18.6 0.37 1.10 18.6 0.39 1.10 19.5 0.41 1.10 20.4 λ = 532nm (constant value) n = 1 (constant value)

5

Sinθ(deg) 0.311

D(m) 1.71

0.346 0.346 0.33 0.34

1.56 1.56 1.59 1.52

HWU Physics investigation Student handbook Page 26

9|Page Richard Donaldson – Advanced Higher Physics

Calculations Equation:

λ = 532 x 10-9m sinθ = sin(19.5) = 0.33 n=1

(

)

m

Mean value

Where:      

n is the order of the maximum λ is the wavelength of light d is the track spacing (separation of slits) θ is the angle from the zero order to the nth maximum A is the central order, B is the first order maximum Length AB is the opposite side, length AC is the adjacent

C θ

A

Calculation of Uncertainties Metre stick Scale reading: 0.005mm Calibration: 0.01mm Total uncertainty

√

=√

Fringe width Random uncertainty:

= 0.002

Error bars were not plotted on the graph due to the uncertainty’s being too small to be accurately plotted Uncertainty in d Using the linest function, I was able to calculate that the overall uncertainty in d was: m So overall. The value that I calculated for the track spacing of a CD was: m

10 | P a g e R i c h a r d D o n a l d s o n – A d v a n c e d H i g h e r P h y s i c s

B

Experiment 3: Diameter of human hair

Aim: To calculate the diameter of a human hair using diffraction. Method:

Strand of hair Screen

Laser

D Set up the equipment as shown above. Place the hair about 5cm away from the laser. Measure the distance from the hair to the screen and record It as D. turn the laser on and position it so that the beam is hitting the hair and the interference/diffraction pattern is shown on the screen. Measure the length of the central fringe and record it as ω. The diameter (d) can then be calculated using the appropriate equation. 6

Results D(m) 1 0.90 0.80 0.70 0.60 Wavelength – 532nm (constant value)

ω(mm) 13 11 10 9 8

d(μm) 41 43.5 42 41 40

Calculations

  

6

D=1 λ=532nm ω=13

Tyler, F. (1971). A Laboratory Manual of Physics SI Units page 67

11 | P a g e R i c h a r d D o n a l d s o n – A d v a n c e d H i g h e r P h y s i c s

Calculations of uncertainties Metre stick Scale reading: 0.005mm Calibration: 0.01mm Total uncertainty

√

=√

Uncertainty in d Using the linest function, I was able to calculate that the total source of error in d was:

So overall, the value for the diameter of a human hair I calculated was: (

12 | P a g e R i c h a r d D o n a l d s o n – A d v a n c e d H i g h e r P h y s i c s

Investigation Conclusion & Evaluation Conclusion: The values that I have obtained from the three experiments I conducted are as follows: Wavelength of Sodium light Diameter of human hair Track spacing of a CD:

( m

The values that I have found are correct values as the wavelength of sodium light is 589nm. Although there is a difference of 3nm between my value and the actual value, due to the nature of how the wavelength corresponds to its colour, the value I calculated is still the value of Sodium light. The Diameter of human hair varies between person to person, so there is no exact value for the diameter. The track spacing of a CD also varies depending on the capacity of the CD and whether or not it is duel layer, however doing research over the internet, the average value for the track spacing meeting the conditions of my CD (duel layered disk), the actual value was the value that I found. I have conducted this investigation in order to show how the interference of light can be used in finding wavelength, diameter and the track spacing of a CD. My first experiment used an interference pattern known as Newton’s rings in order to determine the wavelength of sodium light. My second experiment used diffraction in order to determine the track spacing of a standard CD. My third experiment also used diffraction to determine the diameter of a human hair. My first experiment was difficult for me to conduct as it required equipment that had to be set up perfectly with no room for error in order to conduct it, this was challenging as the setup of the experiment was time consuming and some faults in my equipment occurred. Despite these drawbacks, the first experiment uses a very simple principle and with the improvements that I suggested, the results could be easier to find and more accurate. My second and third experiments were in contrast to my first experiment as they were both easy to set up and gaining results was easy. Overall this experiment has been a success as I have conducted the three experiments and developed results to the best of my ability. Discussion and Evaluation: There were some problems I ran into while trying to set up this experiment. On some runs, the interference pattern was difficult to view through the travelling microscope as the pattern was too small to be observed accurately. I decided to take the experiment apart and make sure all my equipment was clean and working correctly. I then attempted the experiment again, with greater results, as the interference pattern was visible. Another problem I ran into on a few attempts was the crosshair on the travelling microscope was not visible enough to get accurate results. However, once I was able to overcome these issues, I was able to get results. Some improvements that could have been made to this experiment could have been to use a camera to take pictures of the interference pattern and then use tracker software on a computer to measure the diameters of each of the rings. This would mean that the diameters would be 13 | P a g e R i c h a r d D o n a l d s o n – A d v a n c e d H i g h e r P h y s i c s

measured more accurately that with using a travelling microscope, which would in turn make the calculation for the wavelength more accurate. Some possible sources of error could be if the glass plates and plano-convex lens aren’t cleaned properly. This could affect the clarity of the interference pattern, which could in turn affect the results. If the travelling microscope is not moved in the same direction each time the experiment is conducted, a back lash error could occur, which would affect the results. Out of the three experiments I conducted, the second experiment; track spacing of a CD was the easiest to get results as the equipment is easy to set up and the methods taken to get results are basic. Some improvements that could be made are that some possible sources of error could have been If the beam of the laser is not positioned at about centre on the CD, the reflected beam would be in a position on the screen in which results could not be taken, for example, if the laser beam is positioned too low, the beam of light would be reflected in the horizontal, which would not allow the track spacing to be calculated.

On my third experiment, one change I made was to use a laser as a light source, rather than a extended light source. This was due to a lack of equipment as no narrow slits were able, so I could not focus the light from the extended source onto the hair. Some improvements that could have been made to this experiment could have been to use an optical bench in order to get more accurate results. Some possible sources of error for this experiment could have been if the hair was moved at all during the measurement of the fringe width. As the hair is so small, it is easily affected by air or any movement nearby. Therefore it is crucial that hair must not move as much as possible in order to get accurate results.

14 | P a g e R i c h a r d D o n a l d s o n – A d v a n c e d H i g h e r P h y s i c s

References Figure 1: Tyler, F. (1971). A Laboratory Manual of Physics SI Units. Edward Arnold.  

Page 74 Page 67

Express, S. (n.d.). Proof of nlambda = dsintheta. Retrieved November 07, 2013, from www.studentxpress.ie: www.studentxpress.ie/proof1.pdf Tyler, F. (1971). A Laboratory Manual of Physcis SI Units. Edward Arnold. University, H. W. (2009/2010). Retrieved October 2013, from http://physicskyle.files.wordpress.com/2011/06/ah-physics-investigation1.pdf 

Page 26

15 | P a g e R i c h a r d D o n a l d s o n – A d v a n c e d H i g h e r P h y s i c s