Question

On placing a thin sheet of mica of 1.2 $\mu$m thickness in the path of one of the interfering beams in a bi-prism experiment, it is found that the central bright band shifts to a distance equal to the width of a bright fringe. The refractive index of mica is $\frac{x}{2}$. Find $x$. ($\lambda =600$ nm).

Answer 1

The width of the bright fringe is given by : $\frac{\lambda D}{d}$

The shift in central maxima due to placing mica is given by : $\frac{(\mu -1)tD}{d}$

It is given that the shift is equal to the length of a bright fringe.

$\frac{\lambda D}{d}$ = $\frac{(\mu -1)tD}{d}$

$\frac{600D}{d}$ = $\frac{(\mu -1)1200D}{d}$

$\mu$ = 1 + $\frac{1}{2}$ = $\frac{3}{2}$

$\therefore$ x = 3