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1. Using the configuration shown in Figure 1, show that: mλ = dsin(0), (1) where A is the wavelength of incident light, d is the center-to-center separation of the slits, and is the angle as shown. 2. Then show that the spacing Ay between adjacent bright fringes appearing on the screen a distance D away from the slits is: Ay = Dª (2) Hint: The path-length difference corresponding to adjacent bright fringes is X, and you can assume small angles so sin 00. Make sure to include a diagram and discuss all approximations made for this expression to be valid.

1. Using the configuration shown in Figure 1, show that: mλ = dsin(0), (1) where A is the wavelength of incident light, d is the center-to-center separation of the slits, and is the angle as shown. 2. Then show that the spacing Ay between adjacent bright fringes appearing on the screen a distance D away from the slits is: Ay = Dª (2) Hint: The path-length difference corresponding to adjacent bright fringes is X, and you can assume small angles so sin 00. Make sure to include a diagram and discuss all approximations made for this expression to be valid.

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answer both part 1 and 2

Part 1: Double-Slit Interference In lecture you studied Thomas Young's classic double-slit experiment. A basic analysis of this experiment follows. When monochromatic and coherent (i.e. in-phase) light is incident on a pair of slits, the transmitted light appears as two separate sources that propagate, in-phase, to a distant screen. The resulting pattern on the screen (Figure 1) consists of a series of bright and dark stripes called “interference” fringes. The fringes result from the different path lengths taken by the two separate waves. For an "in-phase" condition to exist (bright stripe on the screen; "constructive interference"), the path length difference AL must be an integer number of wavelengths, mλ. Conversely, if the path length difference for the two waves is exactly m(), the waves will effectively cancel each other at the screen ("destructive interference"), forming a dark stripe. The exact fringe pattern observed on a fixed screen depends on both the wavelength of incident light and the double-slit spacing. Incoming Light AL D Figure 1: Geometric construction of Young's Double-Slit Experiment.
Transcribed Image Text:Part 1: Double-Slit Interference In lecture you studied Thomas Young's classic double-slit experiment. A basic analysis of this experiment follows. When monochromatic and coherent (i.e. in-phase) light is incident on a pair of slits, the transmitted light appears as two separate sources that propagate, in-phase, to a distant screen. The resulting pattern on the screen (Figure 1) consists of a series of bright and dark stripes called “interference” fringes. The fringes result from the different path lengths taken by the two separate waves. For an "in-phase" condition to exist (bright stripe on the screen; "constructive interference"), the path length difference AL must be an integer number of wavelengths, mλ. Conversely, if the path length difference for the two waves is exactly m(), the waves will effectively cancel each other at the screen ("destructive interference"), forming a dark stripe. The exact fringe pattern observed on a fixed screen depends on both the wavelength of incident light and the double-slit spacing. Incoming Light AL D Figure 1: Geometric construction of Young's Double-Slit Experiment.
1. Using the configuration shown in Figure 1, show that: mλ = dsin(0), (1) where X is the wavelength of incident light, d is the center-to-center separation of the slits, and is the angle as shown. 2. Then show that the spacing Ay between adjacent bright fringes appearing on the screen a distance D away from the slits is: Ay = D. D=1 (2) Hint: The path-length difference corresponding to adjacent bright fringes is λ, and you can assume small angles so sin 0≈ 0. Make sure to include a diagram and discuss all approximations made for this expression to be valid.
Transcribed Image Text:1. Using the configuration shown in Figure 1, show that: mλ = dsin(0), (1) where X is the wavelength of incident light, d is the center-to-center separation of the slits, and is the angle as shown. 2. Then show that the spacing Ay between adjacent bright fringes appearing on the screen a distance D away from the slits is: Ay = D. D=1 (2) Hint: The path-length difference corresponding to adjacent bright fringes is λ, and you can assume small angles so sin 0≈ 0. Make sure to include a diagram and discuss all approximations made for this expression to be valid.
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