A single slit of width a is illuminated by light of wavelength λ. If a = 4.3λ, the maximum number of dark fringes on a semi-circular screen surrounding the slit is
A) 2.
B) 4.
C) 6.
D) 8.
E) 9.

Question

Quizplus · Accepted Answer

The number of dark fringes in a diffraction pattern is given by the formula:
n = (2a/λ) sinθ
where n is the number of dark fringes, a is the width of the slit, λ is the wavelength of light, and θ is the angle between the central maximum and the nth dark fringe. 
For a semi-circular screen surrounding the slit, the angle θ is π/2. 
Thus, n = (2a/λ) sin(π/2) = 2a/λ 
Substituting a = 4.3λ, we get n = 8.6. 
Since the number of fringes must be an integer, the maximum number of fringes on the screen is 8, so the answer is D.

A Single Slit of Width a Is Illuminated by Light