Question

Light of wavelength 670 nm falls on two slits and produces an interference pattern in which the third-order bright fringe is 45 mm from the central fringe on a screen 3.3 m away.

What is the separation of the two slits?

Answer 1

Solution:

Given:

Wavelength (λ) = 670 nm = 670 x 10^-9 m

L = 3.3 m

y₃ = 45 mm = 45 x 10^-3 m

The expression for constructive interference in the double-slit experiment is

d Sin θ = m λ

But, for smaller angles : sinθ = tan θ = y/L

d y/L = m λ

d = m λ L / y₃

d = (3)(670 x 10^-9 m)(3.3 m) / (45 x 10^-3 m)

d = 147.4 x 10^-6 m or   d = 0.147 mm