To ensure almost 100 per cent transitivity, photographic lenses are often coated with a thin layer of dielectric material. The refractive index of this material is intermediated between that of air and glass (which makes the optical element of the lens). A typically used dielectric film is MgF 2 (n = 1.38). What should the thickness of the film be so that at the center of the visible spectrum (5500 Å) there is maximum transmission.

To ensure almost 100 per cent transitivity, photographic lenses are often coated with a thin layer of dielectric material. The refractive index of this material is intermediated between that of air and glass (which makes the optical element of the lens). A typically used dielectric film is MgF₂ (n = 1.38). What should the thickness of the film be so that at the center of the visible spectrum (5500 Å) there is maximum transmission.

Given λ = 5500 Å, refractive index of film = 1.38, refractive index of glass =1.5

Let d be the thickness of the dielectric film deposited on a glass lens, incident angle be θi and refracted angle be θr.

A part of this ray is reflected as r1 from the air-film interface and a part refracted inside. The refracted ray inside get reflected at film-glass interface and a part is refracted at the film-air interface and transmitted as r2

If incident light is to be transmitted through the lens, r1 and r2 should interfere destructively. The reflection from both A and D are from lower to higher refractive index and hence, there is no phase change on reflection.

Here, optical path difference between r2 and r1, is given by

From figure,

We know,

Substituting in OPD

In order to interfere destructively, the path difference should be λ/2

For photographic lenses, the sources are normally in vertical plane i.e.