1 answer

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

Question:

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


Answers

(A)   sinθ =   1.22 λ /d   
                    θ = sin-1 (1.22 λ /d ) .................(1)
Here d = diametre of the pin hole = 0.1*10-3 m
wave length λ =   632.8*10-9 m  
             θ = 0.4420
(B) when θ is small   
             tanθ   = sinθ = y / L
Radius of the first dark fringe y   = Ltanθ   =   ( 3m )( tan   0.4420 )   = 0.023.2 m =   23.2 mm
(C) Area     = πy2   = 3.14 ( 0.023.2 m ) 2 = 1690.0736( mm)2
.

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