PHYS 1402 DIFFRACTION AND INTERFERENCE OF LIGHT: MEASURE THE WAVELENGTH OF LIGHT

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1 PHYS 1402 DIFFRACTION AND INTERFERENCE OF LIGHT: MEASURE THE WAVELENGTH OF LIGHT I. OBJECTIVE The objective of this experiment is to observe the interference pattern from a double slit and a diffraction patterns from a single slit and a diffraction grating. In each case, measurement of the distance between the dark fringes or bright fringes projected on the screen allows us to calculate the wavelength of the laser source used. II. APPARATUS Laser, optical bench and optics kit containing double slits, single slits, diffraction grating and other accessories. III. EXPERIMENTAL PROCEDURE Procedure (1): Interference pattern with double Slit 1. Place laser and double slit on the optical bench and align such that light goes through the double slit. Measure the distance between the double slit and the screen (should be around 1-2m). Call this distance L 2. Observe the interference pattern on the screen. If the pattern is too narrow and the bright and dark fringes are too small to count, then use another double slit which will give you a wider pattern. 3. From the double slit plate, read the slit spacing. This distance is d. Identify the m = 0 bright spot at the center of the pattern. Count bright spots on either side of the center bright spot until you get to a point where the bright spot looks like it is missing. You should be able to count 4 to 5 or more bright spots. Measure the distance between the centers of the outermost bright spots. Call this distance 2y (see Figure (1)). What is m for your case? Take snapshots of the observed interference patterns. 5. Calculate the wavelength of light using the equation given in theory. 7. Compare the measured and the given value of the wavelength of the laser by finding the percent difference. 8. Draw the pattern you observed as a series of bright and dark spots. Label the center bright and the outermost bright spots with their numbers. Procedure (2): Diffraction pattern with single Slit 1. Replace the double slit with a single slit and align on the optical bench. 2. Repeat same procedures you did on the first part to get the measurements of a, y L and m and find the wavelength of the laser using the equation in the theory for single slit diffraction. Note here m is the mth order dark fringe.

2 Procedure (3): diffraction pattern with a Diffraction Grating 1. Replace the single slit with a diffraction grating. A diffraction grating is a piece of plastic with a very large number of slits on it. Align on the optical bench such that the light goes through the grating. 2. Observe the pattern and note differences between it and those of procedures (1) and 3. Measure the distance from grating to screen. Call this distance L. 4. Identify the m = 0 bright spot and the m = 1 bright spots on either side. Measure the distance between the two m = 1 bright spots. Call this distance 2y (see Figure 1) 5. Calculate the angle _1: 6. Calculate the wavelength _ from the condition of constructive interference for the diffraction grating where the slit spacing d is the reciprocal of the number of lines per meter of grating. 7. Compare to the accepted value of the wavelength by calculating the percent difference. 8. Does this procedure give a better result than the previous procedures? 9. Draw a diagram showing the pattern you observed. Label the bright spots with their numbers. On this diagram, show the distances you measured and the angle you calculated.

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4 IV. THEORY

5 In case of constructive interference pattern due to a double slit for the distance of the condition for mth bright fringe ybright from the central maximum is given by Where, d sin θ = mλ sin ϑ = y (y 2 +L 2 ) 1/2 refer to the first figure dy hence small angle approximation: if y <<< L, then the denominator just can be approximated as ml and the wavelength can be written as d y m L Where L is the distance between the slit and the screen where the interference patterns are projected, d is the distance between the two slits and m is the order of the bright fringe considered. Hence the wavelength of the light can be calculated by using the following equation. dy In case of single slit diffraction, the width of the slit is denoted by a instead of d. The wavelength of the light in this case is also given by the following equation, just by replacing d by a. However, in this case the fringe is the dark fringe instead of the bright fringe. ay For a diffraction grating the wavelength of the light is given by dy where d is the distance between two consecutive slits and m is the order of the mth order bright spot from the central maximum. D can be calculated as the following

6 d = (1/number of lines per unit length in the gratings) Note: if small angle approximation is applicable ie (y 2 + L 2 ) 1/2 ~ L, each bright and dark fringe will have equal width and will be separated by equal distance from each other. However, if the above approximation cannot be applied farther the point p is on the screen from the central maximum, larger will be the separation between two nearest bright or dark fringes. We should be able to see this effect in the diffraction grating. V. ANALYSIS 1. For each procedure, record your data in the data table and perform all the necessary calculations. 2. For each procedure, take snapshots of each pattern and label accordingly. 3. Write a conclusion summarizing your results. VI OBSERVATION TABLE Slit to screen distance L (m) Slit Spacing d (m) Order of the fringe m Width of the observed pattern 2y (m) Calculated wavelength λ (m) Theoretical wavelength λ (m) Difference % Double Slit Single Slit Diffraction Grating Questions: 1. What differences you noticed between the interference and the diffraction fringes 2. What happens to the interference or diffraction pattern if d is decreased or increased? 3. How would your observations differ if you were using a green laser? Green laser has lower wavelength.

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