Question

Two thin parallel slits are made in an opaque sheet of film when a monochromatic beam of light is shone through them at normal incidence. The first bright fringes in the transmitted light occur at $\pm {45}^0$ with the original direction of the light beam on a distant screen when the apparatus is in air.When the apparatus is immersed in a liquid,the same bright fringes now occur at $\pm {30}^0$. Find the index of refraction of the liquid.

Answer 1

$\sin \theta =\sin 45°=\frac{1}{\sqrt{a}}=1\times \frac{\lambda }{d}$

In medium,

$\sin 30°=\frac{1}{2}=\frac{\lambda }{d}\times \frac{1}{\mu }\therefore \mu =\frac{1}{\sqrt{2}}$