Question

Laser light of wavelength lambda passes through a thin slit of width a and produces its first dark fringes at angles of +/- 30 degree with the original direction of the beam. The slit is then reduced in size to a circle of diameter a. When the same laser light is passed through the circle, the first dark fringe occurs at

A) +/- 66.9 degree.
B) +/- 45.0 degree.
C) +/- 37.6 degree.
D) +/- 36.6 degree.
E) +/- 15.0 degree.

Answer 1

Answer:

C- ±37.6°

Explanation:

This is the case of a single slit diffraction. In this case, the dark fringe occurs at

sin θ = ± mλ/a

where m = 1

θ = ± 30°

Hence we have sin ± 30° = ± λ/a

±0.5 = ± λ/a

Hence, we have a = 2λ

For a circular aperture, the condition for the first dark fringe is

D = diameter of circle = a = 2λ

so we have sin θ1 = 1.22λ/a

sin θ1 = 1.22λ/2λ

hence sin θ1 = 0.61

θ1 = sin⁻¹0.61 = ±37.6°