# Diffraction of Laser Light

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1 Diffraction of Laser Light No Prelab Introduction The laser is a unique light source because its light is coherent and monochromatic. Coherent light is made up of waves, which are all in phase. Monochromatic light is a single color or wavelength. The wavelength of the red laser light is 670 nm (nm = nanometer = 10-9 m). In this experiment, the diffraction patterns of a single slit, a double slit, a human hair, and a circular aperture are examined. Theory Diffraction is produced when light passes through an opening whose size is the same order of magnitude as its wavelength. As the light spreads outward from the opening, the light waves travel different distances, producing an interference pattern at the screen. A bright spot is formed when the light waves interfere constructively and a dark spot is formed when they interfere destructively. For example, in a double slit experiment light from one slit travels a different distance than light from the second slit. A bright spot will be formed if the difference in distances is an integral number of wavelengths. A dark spot will be formed if the difference is a half-integral number of wavelengths (e.g.1/2, 3/2, 5/2, etc.). As can be seen from the above diagram, a bright spot will be formed when r 2 r 1 = mλ = dsinθ. For small angles (where R >> y), sinθ tanθ = y /R, so Pattern produced by a double slit. y = mλr (1) where m = 0, 1, 2, for a bright spot d and m = 1/2, 3/2, 5/2,...for a dark spot. 82

2 Pattern produced by a single slit. For a single slit, the condition for a dark spot is sinθ = mλ /d (2) where d is the width of the slit and m = 1,2,3,... for dark spots. The diffraction pattern produced by a human hair is the same as that which would be produced if a slit the width of the hair were used. If, instead of a single slit, we use a small circular opening of diameter d, we will observe a circular diffraction pattern instead of a linear diffraction pattern. The equation for the minima has the same form as that for the linear case, namely d sinθ = mλ. (3) However, m is no longer an integer but is the zero solutions to first order Bessel function divided by p. That is, m = l.220, 2.233, 3.283, 4.241,... Apparatus 1. laser 4. caliper 2. Single and double slits 3. optical bench, screen Procedure: 1. Double slit experiment: Shine the laser through a double slit and observe the diffraction pattern on a screen across the room. Sketch the pattern on the data sheet and measure the distance between the first minima on either side of the central bright spot. Repeat the measurement for the second minima. Divide the distance by 2 and find the angle Θ, then use Equation (1) to find d. Compare with known value. Repeat for a second slit 2. Single Slit Experiment Shine the laser through a single slit and observe the diffraction pattern. Sketch the pattern on the data sheet. Repeat the measurement in procedure 1 and find d for the slit. Compare with the known value. Repeat for a second single slit 83

3 3. Circular Aperture The diameter of circular opening can be determined by using laser light. Rotate the Slit Disk until the laser light shines through a circular opening. Now place the slits between 6 to 8 cm from the laser and place the screen on the optical bench.l You should see a pattern on the screen characterized by two or three dark rings. Sketch the diffraction pattern and measure the diameter of the ring. From the radius of the rings calculate the angle θ and from Equation (3) find the diameter of the ring. 4. Human hair Data Remove single slit disk and stretch a hair across the opening and tape the hair to the lens holders. Shine a laser across the hair. Repeat the same measurements and sketch as in procedure 1 and 2. Find the diameter of the hair. Double Slit Diffraction: A. First double slit R = B. Second double slit Known value of d = R = Sketch the diffraction pattern below 84

4 Single Slit Diffraction: A. First single slit R = B. Second Single Slit A. % difference = Circular Aperture R = 85

5 Human Hair Diffraction R = QUESTIONS: 1. On the single slit disk, there is a single slit whose width varies as the disk is rotated. How does the distance between the bright and dark spot vary as the disk is rotated from a small value d to a larger value of d? 2. On the double slit disk, the distance between the double slits varies from 0.02 mm to 0.08 mm. How does the distance between the bright and dark spot vary as the disk is rotated from a small value of d to a larger value of d? 86

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