Question

Light with a wavelength of λ = 674 nm. is incident on a single slit of width w = 1.5 micrometers. A screen is located L = 0.95 m behind the slit and an interference pattern has formed on it. What is the distance between the central bright spot and the first dark fringe, D, in meters?

Answer 1

Here, for the distance between the central bright spot and first dark fringe

here, for the first dark fringe

w * sin(theta) = wavelength

1.5 *10^-6 * sin(theta) = 674 *10^-9

sin(theta) = 0.449

theta = 26.7 degree

as tan(theta) = y/D

tan(26.7 degree) = y/0.95

y = 0.48 m

the distance between the central bright spot and first dark firnge is 0.48 m