Question

In Young’s double-slit experiment, using monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by 5 x 10^-2 m towards the slits, the change in the fringe width is 3 x 10^-5 m. If the distance between the two slits is 10-3 m, calculate the wavelength of the light used.

Answer 1

Here, ΔD = 5 x 10^-2 m, Δβ = 3 ×10^-5 m, d = 10^-3 m, λ = ?
We know that fringe width in Young’s double-slit experiment is given by

`"β" = λ "D"/"d"`

Here, since λ and d are constant, we can write

`"Δβ" = λ/"d" "ΔD"`

∴ λ = `"Δβ"/"ΔD" d`

λ = `( 3 xx 10^-5 xx 10^-3)/(5 xx 10^-2)`

λ = `0.6 xx 10^-6 m xx 10^-7 m = 6000Å `