Question

In a Young’s double-slit experiment, let A and B be the two slits. A thin film of thickness t and refractive index μ is placed in front of A. Let β = fringe width. The central maximum will shift

(a) towards A

(b) towards B

(c) by t(μ - 1) β/λ

(d) by μt β/λ

Answer 1

Correct Answer is: (a) towards A, (c) by t(μ - 1) β/λ

Let d = distance between the slits, λ = wavelength of light,

D = distance from the slits to the screen.

For a point P on the screen at a distance x from the centre of the screen, path difference = Δ = x d/D.

Path difference introduced due to film = t(μ - 1).

For central maximum at P, x d/D = t(μ - 1).

or x =  t(μ - 1) D/d.

Now, β = λD/d 

or D/d = β/λ

∴ x = t(μ - 1) β/λ.