Question

A thin paper of thickness $0.02mm$ having a refractive index $1.45$ is pasted across one of the slits in a Young's double slit experiment. The paper transmits $\frac{4}{9}$ of the light energy falling on it. The wavelength of light used is $600nm$. How many fringes will across through the centre if an identical paper-piece is pasted on the other slit also?

Answer 1

Answer: 15

Fringe-width, $\beta =\frac{D\lambda }{d}$
Shifting of fringe pattern due to paper sheet,
$S=\frac{t(\mu -1)D}{d}$
If we paste paper sheet on the other slit, the fringe pattern will shift by same amount on that side.
Hence, number of fringes crossing the centre is
$n=\frac{S}{\beta }$
$=\frac{t(\mu -1)}{\lambda }$
$=\frac{0.02\times 10^{-3}\times (1.45-1)}{600\times 10^{-9}}$
$=\frac{0.02\times 0.45\times 10^6}{600}$
$=15$