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Interference

Pre-Lab Questions Page

1. Read about the principle of superposition in your textbook. Part A: Look at the two waves above and below one another. Add them together and draw the resultant wave below them. Do the same thing for Part B. Part A: Part B:

Resultants

2. What type of interference is this called? Answer for Part A: _____________________ Answer for Part B: _______________________ 3. In Young’s Double-slit experiment, a pattern of light and dark fringes are observed. Light comes from both slits and causes a light or dark fringe. What is different about the two sources of light that causes this phenomenon? 4. In your own words, define Diffraction. 5. In your own words, define wavelength. Draw a small wave and indicate the wavelength.

A simplified explanation of single, double and multi-slit interference The type of interference we will be looking at is the interference of coherent light. Think of the light beams in the following discussion as a single continuous wave, such as a sine wave. This is a good representation of the electric field of the laser light we will be using. Remember, these waves obey the principle of superposition. The Single Slit When a beam of laser light is shined through a single thin slit, interference is observed on a projection screen as in the following picture. Don’t expect to see a pattern like this by shining a flashlight through a slit in a piece of paper. The light must be of a single continuous wavelength, such as laser light and the size of the slit must be close to the same size of the wavelength of the light. In the diagram to the right, imagine light coming in from the left and passing through a thin slit of width a. The Intensity of light on a screen a distance D away is represented by the squiggly line. Compare with the above picture. Two rays of light, one from each side of the slit are shown pointing to a spot on the screen that is a distance y from the center. But you say “Wait! The light is coming from the left, how can it point up to that spot at y?” Remember, that this is a wave phenomenon. Picture water waves from the left hitting a retaining wall that has a break in it. Just as the water waves spread out once they pass the break, so do light waves! Back to the diagram. Since the beams of light come from a different side of the slit, they travel a different distance to the point at y. The electric field sine waves in each beam of light obey the principle of superposition, so the can add up to a bright spot, a dark spot, or something in between. Where the dark spots occur can be found using the following relationship of the experiment: mλ = asinθ, m = 1,2,3,… where λ is the wavelength of the incoming light. θ and a are as shown in the diagram above. From the geometry of the triangles and for small angles of θ, sinθ ≈ y/D. Using this, the equation becomes:

aDmy λ

≈ Dark fringes of a Single Slit

Example of a single slit We shine a Helium-Neon laser through a slit that has a width of a = 0.01cm. On a screen that is 6 meters away we get the interference pattern below. We measure the distance from the center maximum to the second dark spot to be y = 7.6 cm. What is the wavelength of light we are using?

y

m = 3 m = 2 m = 1 m = 3 m = 2 m = 1

TRY IT! Plug the numbers into the single slit equation. Remember to use standard units. Your answer should be 633nm. NOTE: If we used a different color laser light, you would get a different y value for the second dark fringe! The Double Slit What if we shine the light through two slits placed very close together? Each slit has its own single-slit interference pattern as described above, but in addition, they interfere with each other! In the diagram, notice that d is the distance between the slits in the double slit picture. In a similar way to finding the single slit equation for dark fringes we can find an equation for the double slit pattern. NOTE that the double slit equation below may look the same as the single slit equation, but this one is for light fringes. It is for the bright spots!

dDmy λ

≈ m = 0, 1, 2…

Bright fringes of a

Double-Slit Pattern

Double slit continued The y in the Double-Slit formula stated on the previous page is the distance from the central maximum to the bright spot at m = 0, 1, 2…. The bright spots would be evenly spaced if not for the superposition of the single-slit interference pattern over it, as shown below.

m = 1 m = 2

m = 0

y

m = 3

The Diffraction Grating A diffraction grating is a device that has many, many slits. So there is a superposition of many single slit diffraction patterns. The result is that the bright spots are nearly points of light separated by large distances of dark areas as shown below. The formula that gives the distance from the central maximum to the bright spots at m = 1, 2, 3… is the same as that for double- slit interference.

dDmy λ

≈ m = 0, 1, 2…

The Laser you will be using You will be using a tunable laser capable of four different wavelengths. These are: Red λ = 632.8 nm ± 1nm Orange λ = 611.9 nm ± 1nm

Transverse Adjust DO NOT CHANGE

ON/OFF

Color Selector

Yellow λ = 594.1 nm ± 1nm Green λ = 543.0 nm ± 1nm CAUTION: DO NOT LOOK DIRECTLY INTO THE LASER BEAM OR ITS REFLECTION FROM A MIRRORED SURFACE.

Interference Lab Procedure 1. Turn on the laser and let it warm up for 1 minute. You may have to open the aperture to let the beam out. If you see no laser light after one minute, get the instructor. The laser light should be Red. If it is not, adjust the color selector knob slowly until you see it. LASER CONTROLS: The order of light while adjusting the selector knob COUNTER-CLOCKWISE is Green, Yellow, Orange, Red. Do NOT adjust any other controls and do NOT turn the color selector more than 1 full turn. 2. Adjust the position of the rectangular glass piece that has the slits in it using the screws and rod holder so the laser beam hits the glass surface at 90° and hits the Single-Slit hole. You should see a sharp pattern on the far wall. 3. Tape a clean sheet of paper to the wall so the light pattern hits it near the top. You need to make room to trace all three patterns on this single sheet of paper. 4. Using the metric measuring tape, measure the distance between the slits and your paper ‘screen’. 5. Trace the single slit pattern on your paper. Remember, for this one you will be measuring the distance between the center of the pattern and the dark spots. 6. Now adjust the rectangular glass piece so the laser runs through the Double-Slits. Move your paper screen accordingly and trace the pattern on your paper, remembering that you will be measuring the distance between the center of the pattern and the bright spots. 7. Now adjust the rectangular glass piece so the laser runs through the Grating. Move your paper screen accordingly. Mark the bright Red circles. 8. SLOWLY turn the color selector control clockwise NO MORE THAN 1/4 OF A TURN until the color changes to orange. Move your paper and trace the Orange circles. 9. SLOWLY turn the color selector control clockwise NO MORE THAN 1/4 OF A TURN until the color changes to yellow. Move your paper and trace the Yellow circles. 10. SLOWLY turn the color selector control clockwise NO MORE THAN 1/2 OF A TURN until the color changes to green. Move your paper and trace the Green circles. 11. SLOWLY turn the color selector clockwise to bring it back to Red and turn OFF the laser. 12. Record the slit widths and separations for the Single-slit, Double-Slit and Grating as marked on the rectangular glass piece.

Analysis You will now measure the spacing for the dark spots (single-slit) or light spots (double-slit and grating). From these you will calculate the wavelength of the laser light using the appropriate formula. These will then be compared to the known wavelengths given earlier. 1. To calculate the wavelength of light from the single-slit pattern we will use m = 1 and the picture below. However, just taking one measurement will not give a good value for y. Therefore, we will get an average value for y by dividing the length L by the number of segments. (In this picture there are 6 segments, it may be different for you)

m = 1 m = 2 m = 3 m = 1 m = 2 m = 3

y

L Now, using your picture and the formula for Dark fringes of a Single Slit, find the wavelength of light used in your single-slit experiment. Compare this to the accepted value. 2. Repeat what you did in step 1 but now for your double-slit pattern. Two things you should remember are that the double slit formula is for the center of the bright fringes. Also, since the single-slit pattern is superimposed on the double-slit pattern, you may want to find an average value of y by just looking at the central light spots. 3. Calculate the wavelength of light used in each of your diffraction grating patterns. You do not have to compare these to the accepted wavelength. 4. If we call the average spacing between the grating spots ∆X, and use m = 1in the diffraction grating formula. We can write a new formula.

⎟⎠⎞

⎜⎝⎛ ∆=

Dxdλ

Using Graphical Analysis plot a graph of λ vs ∆X/D. Using your value from the graph, find the grating spacing and compare it to the accepted value.