Question

In a double-slit arrangement the slits are separated by a distance equal to 100 times the wavelength of the light passing through the slits.

 (a) What is the angular separation in radians between the central maximum and an adjacent maximum?

(b) What is the distance between these maxima on a screen 50.0 cm from the slits?

Answer 1

Data : d = 100 λ, D = 50.0 cm

a) The condition for maximum intensity in Young's experiment is,

d sin θ = nλ , n = 0, 1, 2...,

The angle between the central maximum and itsadjacent maximum can be determined by setting n equal to 1,

∴ d sin θ = λ

∴ θ = sin⁻¹(λ/d )= sin⁻¹(λ/100λ) = sin⁻¹(1/100) = 0.9’ = 0.01571 rad

(b) The distance between these maxima on the screen is

D sin θ = D(λ/d) = 50(λ/100λ) = 0.50 cm