Question

A plate of thickness t made of a material of refractive index µ is placed in front of one of the slits in a double slit experiment. (a) Find the change in the optical path due to introduction of the plate. (b) What should be the minimum thickness t which will make the intensity at the centre of the fringe pattern zero? Wavelength of the light used is λ. Neglect any absorption of light in the plate.

Answer 1

Given :

thickness of plate= t

refractive index of plate =µ

a)Find the change in the optical path due to introduction of the plate:

optical path difference = (µ-1) t

b)For zero intensity at the centre of the fringe pattern, there should be distractive interference at the centre.

So, the optical path difference should be = λ/2

(µ-1) t=λ/2

t= λ/2(μ-1)

∴ the minimum thickness t which will make the intensity at the centre of the fringe pattern zero is t= λ/2(μ-1)

Answer 2

Explanation:

2(μ−1)/λ

path difference is (μ−1)t

for the intendity to be zero

(μ−1)t=(n+ 21 ) 2/λ

for minimum thickness n=0t= 2(μ−1)λ

option C is correct