In a double slit experiment, when a thin film of thickness $t$ having refractive index $\mu$ is inse

Question

In a double slit experiment, when a thin film of thickness $t$ having refractive index $\mu$ is inserted in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. If $\lambda$ is the wavelength of the light used, the value of $t$ is

Professor PC Thomas Classes · Answer

Shift $\Delta x = \frac{D}{d}(\mu-1)t$. Setting to one fringe width $\frac{\lambda D}{d}$, we get $t = \frac{\lambda}{\mu-1}$.