Question

A glass plate, of refractive index 1.5, is coated with a thin layer of thickness t and refractive index μ₁ = 1.8 . Light, of wave length λ , travelling in air is incident (nearly) normally an the layer. It is partly reflected at its upper and lower ends and the two reflected rays interfere. If λ = 648 nm, the minimum value of t, for which constructive interference would take place, is

(1) 45 nm

(2) 60 nm

(3) 90 nm

(4) 108 nm

Answer 1

(2) 60 nm

In Fig PQRS is the glass plate and PQQ₁ P₁ is the thin fim. AB is the (nearly normally) incident ray. BR is the reflected ray from the upper end and CD is the reflected ray at the lower and (P₁Q₁). DE is the corresponding emergent ray. Interference occurs between BR and DE. The path difference

Δ ≃ 2μ₁t

There is an additional path difference of λ/2 due to reflection at PQ (reflection from the boundary of a denser medium). There is no extra path difference due to reflection at P₁Q₁ , as this reflection is from the boundary of a rarer medium. For constructive interference, we therefore, have

For minimum value of t, n = 1. Therefore