Question

A glass plate of refractive index 1.5 is coated with a thin layer of thickness d and refractive index 1.8. Light of wavelength λ travelling in air is incident normally on the layer. It is partly reflected at the upper and lower surfaces of the layer and the two reflected rays interfere. Write the condition for their constructive interference. If λ = 648 nm obtain the least value of d for which the rays interfere constructively.

Answer 1

Glass-coating interference (Fig. 12.21) is just like airglass interference. (see Fig. 12.8)

The path difference between AR1 and BR2 is

The first ray AR₁ undergoes a phase change of π which corresponds to a path difference of λ/2.

For constructive interference