Question

A ray from medium 1 is refracted below while passing to medium 2. Find the refractive index of the second medium with respect to medium 1.

Answer 1

From the given figure it is clear that

angle of incidence, $i={30}^{\circ }$

angle of refraction, $r={45}^{\circ }$

Refractive index of medium 2 with respect to medium 1 = ${}^1{\mu }_2$

Applying snell's Law, we get

${\mu }_1\sin i={\mu }_2\sin r⟹{\mu }_1\sin \left({30}^{\circ }\right)={\mu }_2\sin \left({45}^{\circ }\right)⟹{\mu }_1\times \frac{1}{2}={\mu }_2\times \frac{1}{\sqrt{2}}⟹\frac{{\mu }_2}{{\mu }_1}=\frac{\sqrt{2}}{2}⟹\frac{{\mu }_2}{{\mu }_1}=0.707$

Hence the refractive index of the second medium with respect to medium 1 is 0.707.