Determination of the Thickness of a Thin Film by Fresnel’s Biprism

In this experiment, the thickness of a thin film is determined with the help of Fresnel’s biprism.

Suppose the central bright fringe, which is initially formed at P₀, is observed on the screen. Let the distance between the virtual coherent sources S₁ and S₂ be d, and the distance between the virtual sources and the screen be D.

A transparent thin film of thickness t and refractive index μ is introduced in the path of one of the interfering beams. Due to the introduction of the film, the central bright fringe is displaced from P₀ to P₁ through a distance x.

The optical path difference produced due to the thin film is:

(μt − t) = t(μ − 1)

The path difference corresponding to the displacement x of the fringe is:

^xd⁄_D

Therefore,

t(μ − 1) = ^xd⁄_D

Hence,

t = ^xd⁄ _{D(μ − 1)}    (1) 

(Thickness with help of path difference)

Case (i) If the displaced fringe is the n^th bright fringe, then the path difference is:

t(μ − 1) = nλ

Therefore,

t = ^nλ⁄ _{(μ − 1)}    (2) 

Case (ii) Similarly, if the central fringe is displaced to the position of the n^th dark fringe, then:

t(μ − 1) = ^{(2n − 1)λ}⁄₂

Therefore,

t = ^{(2n − 1)λ}⁄ _{2(μ − 1)}    (3)

Using equations (1), (2) and (3), the thickness of the thin film, or the wavelength of monochromatic light, can be determined if the other required quantities are known.