Home/ Questions/Part A: At what angle θ1  to the normal would the first dark ring be observed? answer is .442o Part B: Suppose...
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Asked: 2022-04-13T09:24:02+00:00 In:

Part A: At what angle θ1  to the normal would the first dark ring be observed? answer is .442o Part B: Suppose…

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Part A: At what angle θ1  to the normal would the first dark ring be observed?

answer is 442o

Part B: Suppose that the light from the pinhole projects onto a screen 3 meters away. What is the radius of the first dark ring on that screen? Notice that the angle from Part A is small enough that sinθ≈tanθ .

Answer is 23.2mm

Part C: The first dark ring forms the boundary for the bright Airy disk at the center of the diffraction pattern. What is the area A of the Airy disk on the screen from Part B? answer must be in mm2

♦ Relevant knowledge
The curvature of light that occurs when moving from one medium to another medium is known as refraction. When light from white travels through a glass, dispersion of colors is seen because of different refractive indices that the medium provides for various shades.

 

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  1. Best Answer
    (A) Sinθ = 1.22 λ /d
    θ = sin -1 (1.22 λ /d) ……………..(1)
    Here d = diameter of the pin hole = 0.1 × 10-3 m
    Wave length λ = 632.8 × 10 -9
    θ = 0.442 0
    (B) when θ is small
    tan θ = sin θ = y / L
    Radius of the first dark fringe = Ltanθ = (3m )( Tan 0.442 0) = 0.0232m = 23.2mm
    (C) Area = πy 2 = 3.14 (0.03232 m) 2 = 1690.0736 ( mm) 2
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