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

Question

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

answer is 442^o

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

[su_box title="♦ Relevant knowledge" box_color="#2d6ff7" radius="1"]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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Charlotte O'Ryan · Accepted 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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