Part A: At what angle 1 to the normal would the first dark ring be observed? ans

Question

Part A: At what angle 1  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 sintan .

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

Explanation / Answer

(A)   sin =   1.22 /d                        = sin-1 (1.22 /d ) .................(1) Here d = diametre of the pin hole = 0.1*10-3 m wave length =   632.8*10-9 m                = 0.4420 (B) when is small                 tan   = sin = y / L Radius of the first dark fringe y   = Ltan   =   ( 3m )( tan   0.4420 )   = 0.023.2 m =   23.2 mm (C) Area     = y2   = 3.14 ( 0.023.2 m ) 2 = 1690.0736( mm)2

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