Question

A transparent paper (refractive index $=1.45$) of thickness $0.02mm$ is pasted on one of the slits of Young's double slit experiment which uses monochromatic light of wavelength $620nm$. How many fringes will cross through the centre if the paper is removed?

Answer 1

Given

The refractive index of the paper is $\mu =1.45$

Thickness of the paper is $t=0.02mm=0.02\times {10}^{-3}m$

and the wavelength of the light used is $\lambda =620nm=620\times {10}^{-9}m$

We know, when the transparent paper is pasted in one of the slits, the optical path changes by $(\mu -1)t$.

Again, for a shift of one fringe, the optical path should be changed by $\lambda$.

So, no. of fringes crossing through the centre is given by,

$n=\frac{(\mu -1)t}{\lambda }$

$=\frac{0.45\times 0.02\times {10}^{-3}}{620\times {10}^{-9}}=14.5$