Question

Using analytical method, obtain an expression for the fringe width of two interfering waves.

Answer 1

Let,

S₁ and S₂ are two coherent sources separated by a distance d

D = distance between slits and screen

λ = wavelength of light used

P = central point on screen (path difference = 0)

Q = any point at a distance x from P

Path difference at point Q:

Δx = S_2​Q − S_1​Q

From the geometry of the figure,

Δx = `(x d)/D`

For constructive interference:

Δx = nλ

`(x d)/D` = nλ

x_n = `(n lambda D)/d`

This gives the position of the nth bright fringe.

Fringe width = distance between two successive bright fringes

β = x_n+1​ − x_n​

β = `((n + 1)lambda D)/d - (n lambda D)/d`

Fringe width (β) = `(lambda D)/d`