Question

In a double-slit experiment, 6^th dark fringe is observed at a certain point of the screen. A transparent sheet of thickness t and refractive index n is now introduced in the path of one of the two interfering waves to increase its phase by 2π (n − 1) t/λ. The pattern is shifted and 8^th bright fringe is observed at the same point. Find the relation for thickness t in terms of n and λ.

Answer 1

A phase shift of 2π (n − 1) t/λ causes the 6th dark fringe to shift to the position of the 8^th bright fringe.

A dark fringe occurs at:

d sinθ = `(m + 1/2)lambda`

A bright fringe occurs at:

d sinθ = mλ

The net shift is given by:

6 + 1/2 + 2π(n − 1) × t/λ = 8

6.05 + 2π(n − 1) × t/λ = 8

2π(n − 1) × t/λ = 8 − 6.5

2π(n − 1) × t/λ = 1.5

t = `(3 lambda)/(4 pi(n - 1))`