answer both part 1 and 2 Part 1: Double-Slit InterferenceIn lecture you studied Thomas Young's classic double-slit experiment. A basic analysis of this experiment follows. Whenmonochromatic and coherent (i.e. in-phase) light is incident on a pair of slits, the transmitted light appears as two separatesources that propagate, in-phase, to a distant screen. The resulting pattern on the screen (Figure 1) consists of a seriesof bright and dark stripes called “interference” fringes. The fringes result from the different path lengths taken by the twoseparate waves. For an "in-phase" condition to exist (bright stripe on the screen; "constructive interference"), the path lengthdifference AL must be an integer number of wavelengths, mλ. Conversely, if the path length difference for the two waves isexactly 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-slitspacing.Incoming LightALDFigure 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 theslits is:Ay = D.D=1(2)Hint: The path-length difference corresponding to adjacent bright fringes is λ, and you can assume small angles sosin 0≈ 0.Make sure to include a diagram and discuss all approximations made for this expression to be valid.

Question

answer both part 1 and 2 Part 1: Double-Slit InterferenceIn lecture you studied Thomas Young's classic double-slit experiment. A basic analysis of this experiment follows. Whenmonochromatic and coherent (i.e. in-phase) light is incident on a pair of slits, the transmitted light appears as two separatesources that propagate, in-phase, to a distant screen. The resulting pattern on the screen (Figure 1) consists of a seriesof bright and dark stripes called “interference” fringes. The fringes result from the different path lengths taken by the twoseparate waves. For an &#34;in-phase&#34; condition to exist (bright stripe on the screen; &#34;constructive interference&#34;), the path lengthdifference AL must be an integer number of wavelengths, mλ. Conversely, if the path length difference for the two waves isexactly m(), the waves will effectively cancel each other at the screen (&#34;destructive interference&#34;), forming a dark stripe.The exact fringe pattern observed on a fixed screen depends on both the wavelength of incident light and the double-slitspacing.Incoming LightALDFigure 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 theslits is:Ay = D.D=1(2)Hint: The path-length difference corresponding to adjacent bright fringes is λ, and you can assume small angles sosin 0≈ 0.Make sure to include a diagram and discuss all approximations made for this expression to be valid.

Accepted Answer

Answered: Image /qna-images/answer/7d634209-b05a-4442-bc44-e03e1bf4e9d1.jpg