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Interference and Diffraction of Light

Equipment:

1 1 1 1 1 1 1 1 1 INCLUDED: Basic Optics Track, 1.2 m High Precision Diffraction Slits Basic Optics Diode Laser Aperture Bracket Linear Translator High Sensitivity Light Sensor Rotary Motion Sensor 850 Universal Interface PASCO Capstone OS-8508 OS-8453 OS-8525A OS-8534B OS-8535 PS-2176 PS-2120 UI-5000 UI-5400

Introduction:

The interference maxima for double slits is measured by scanning the laser pattern with a Light Sensor and plotting light intensity versus distance. These measurements are compared to theoretical values. Differences and similarities between interference and diffraction patterns are examined.

Written by Chuck Hunt

Interference and Diffraction EX-5545

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Theory

Single Slit Diffraction When diffraction of light occurs as it passes through a slit, the angle to the minima (dark spot) in the diffraction pattern is given by a sin θ = mλ (m=1,2,3, …) Eq. (1)

where "a" is the slit width, θ is the angle from the center of the pattern to a minimum, λ is the wavelength of the light, and m is the order (m = 1 for the first minimum, 2 for the second minimum, ...counting from the center out). In Figure 1, the laser light pattern is shown just below the computer intensity versus position graph. The angle theta is measured from the center of the single slit to the first minimum, so m equals one for the situation shown in the diagram. Notice that the central spot in the interference Figure 1: Single-Slit Diffraction pattern is twice as wide as the other spots since m=0 is not a minimum. Since theta is a very small angle, sin θ ≅ tan θ = xm/L, where xm is the distance from the center of central maximum to the mth minimum on either side of the central maximum and L is the distance from the slit to the screen. Equation 1 now becomes mλ = a sin θ = a tan θ = axm/L Eq. (2)

It is easier to measure the distance (2xm) from the mth minimum on one side to the mth minimum on the other side than to try to judge the center of the pattern. Equation 2 becomes: mλ = a(2xm)/2L Eq. (3)

Our accuracy will be improved by making (2xm) as large as possible. The slit width is not known very well. The uncertainty in the width is +/- 0.005 mm. That is a 25% uncertainty for the 0.020 mm slit. So instead of using the slit width to calculate a value for the laser wavelength, we use the known wavelength of the laser to calculate a more accurate value for the slit width. Rearranging Equation 3 yields: a = 2mLλ/(2xm) Eq. (4)

Written by Chuck Hunt

Interference and Diffraction EX-5545

Page 3 of 8

Double-Slit Interference When interference of light occurs as it passes through two slits, the angle from the central maximum (bright spot) to the side maxima in the interference pattern is given by d sinθ = nλ (n=0,1,2,3, …) Eq. (4)

where "d" is the slit separation, θ is the angle from the center of the pattern to the nth maximum, λ is the wavelength of the light, and n is the order (0 for the central maximum, 1 for the first side maximum, 2 for the second side maximum ...counting from the center out). In Figure 2, the laser light pattern is shown just below the computer intensity versus position graph. The angle theta is measured from the midway between the double slit to the second side maximum, so n equals two for the situation shown in the diagram. Figure 2: Double-Slit Interference As before, theta is a small angle and Equation 4 may be rewritten: nλ = d sinθ = d tanθ = dxn/L Eq. (5)

where xn is the distance from the central maximum to the nth side maximum and L is the distance from the slits to the screen. The distance from one max to the next (∆x) is then:

∆x = xn+1 – xn = (n+1)λL/d -nλL/d = λL/d

Eq. (6)

Note that ∆x does not depend on n, so all the bright spots have the same max to max distance. Since ∆x is small, accuracy will be improved if we measure the distance (n∆x) from the nth...

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