Question

A thin paper of thickness $0.02\, mm$ 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 $600\, nm$. How many fringes will across through the centre if an identical paper-piece is pasted on the other slit also?

Answer 1

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
$n =\frac{ S }{\beta}$
$=\frac{ t (\mu-1)}{\lambda}$
$=\frac{0.02 \times 10^{-3} \times(1.45-1)}{600 \times 10^{-9}}$
$=\frac{0.02 \times 0.45 \times 10^{6}}{600}$
$=15$