A beam of wavelength passes through a single slit of width and produces its first…

PHYSICS · Single correct · A Level · Physics · Waves · Waves

Problem

A beam of wavelength

\lambda

passes through a single slit of width

a

and produces its first dark fringe at a small angle

\theta

from the central maximum on a distant screen. If the slit width is doubled to

2a

while the wavelength remains the same, what happens to the angular position

\theta'

of the first dark fringe? (Assume

\theta

and

\theta'

are small enough that

\sin\theta\approx\theta

.) (a)

\theta'\;\approx\;2\theta

(b)

\theta'\;\approx\;\dfrac{\theta}{2}

(c)

\theta'\;\approx\;\theta

(d)

\theta'\;\approx\;4\theta