# Interference A simplified explanation of single, double and multi-slit interference

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1 Interference A simplified explanation of single, double and multi-slit interference The tpe 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 obe the principle of superposition. The 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 b 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 Intensit of light on a screen a distance D awa is represented b the squiggl line. Compare with the above picture. Two ras of light, one from each side of the slit are shown pointing to a spot on the screen that is a distance from the center. But ou sa Wait! The light is coming from the left, how can it point up to that spot at? 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 the pass the break, so do light waves! Back to the diagram. Since the beams of light come from a different side of the slit, the travel a different distance to the point at. The electric field sine waves in each beam of light obe 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: m = asin, m = 1,2,3, where is the wavelength of the incoming light. and a are as shown in the diagram above. From the geometr of the triangles and for small angles of, sin /D. Using this, the equation becomes: a Dark fringes of a

2 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 awa we get the interference pattern below. We measure the distance from the center maximum to the second dark spot to be = 7.6 cm. What is the wavelength of light we are using? m = 3 m = 2 m = 1 m = 1 m = 2 m = 3 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, ou would get a different value for the second dark fringe! The What if we shine the light through two slits placed ver close together? Each slit has its own single-slit interference pattern as described above, but in addition, the interfere with each other! In the diagram, notice that d is the distance between the slits in the double slit picture. In a similar wa to finding the single slit dark fringes we can find an equation for slit pattern. NOTE that the double slit below ma look the same as the single slit but this one is for light fringes. It is for the spots! equation for the double equation equation, bright d m = 0, 1, 2 Bright fringes of a Double-Slit Pattern

3 Double slit continued The 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 evenl spaced if not for the superposition of the single-slit interference pattern over it, as shown below. m = 3 m = 2 m = 1 m = 0 The Diffraction Grating A diffraction grating is a device that has man, man slits. So there is a superposition of man single slit diffraction patterns. The result is that the bright spots are nearl points of light separated b large distances of dark areas. 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 doubleslit interference. d m = 0, 1, 2 The Laser ou will be using You will be using metrologic neon laser red laser and green pen laser with tripod. These are: Red = nm Green = nm CAUTION: DO NOT LOOK DIRECTLY INTO THE LASER BEAM OR ITS REFLECTION FROM A MIRRORED SURFACE.

4 Interference Lab Procedure 1. Using the metric measuring tape, measure and record the distance, D between the slits and where the laser will be projected on the wall. 2. Turn on the metrologic neon laser red laser. DO NOT LOOK DIRECTLY INTO THE LASER BEAM OR ITS REFLECTION FROM A MIRROR SURFACE. 3. 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. 4. 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. DO NOT LOOK DIRECTLY INTO THE LASER BEAM OR ITS REFLECTION FROM A MIRROR SURFACE. 5. Trace the single slit pattern on our paper. Remember, for this one ou 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 our paper screen accordingl and trace the pattern on our paper, remembering that ou 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 our paper screen accordingl. Mark the bright Red circles. 8. Turn off the red laser and now repeat steps 2-7 for the green pen laser with using the tripod to kept the laser on and stead. 9. Measure and record the slit widths and separations for the Single-slit, a, Double-Slit and Grating, d, as marked on the rectangular glass piece. 10. 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. Therefore, we will get an average value for b dividing the length L b the number of segments. (In this picture there are 6 segments, it ma be different for ou) m = 3 m = 2 m = 1 m = 1 m = 2 m = 3 L 11. Two things ou should remember are that the double slit formula is for the center of the bright fringes. The singleslit pattern is superimposed on the double-slit pattern, so find an average value of b using just the central light spots.

5 DATA TABLE: Interference Lab Sheet 1 Average a d D Calculations: 1. Now, using each of our pictures and the formula for Dark fringes of a, find the wavelength of light used in our single-slit experiment. Show calculations below. a 2. Compare this using the percent error formula to the theoretical values of the wavelengths. 3. Repeat what ou did in Calculation 1&2 but now for our double-slit pattern. 4. Calculate the wavelength of light used in each of our diffraction grating patterns. You do not have to compare these to the theoretical wavelength. RESULTS TABLE: Experimental λ Theoretical λ Percent Error CONCLUSION: TURN INTERFERENCE LAB SHEET 1 TRACE PATTERNS.

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