Question

A ray of light falls on a transparent sphere with centre at $C$ as shown in figure. The ray emerges from the sphere parallel to line $AB$. Find the refractive index of the sphere.

Answer 1

Refer image.

Where $\mu =$ refractive index

${\mu }_2>{\mu }_1$

Applying snell's law

${\mu }_1\sin {\theta }_1={\mu }_2\sin {\theta }_2$

Where

${\theta }_1=i$ (angle of incidence)

${\theta }_2=r$ (angle of reflection)

$\frac{\sin i}{\sin r}=\frac{{\mu }_2}{{\mu }_2}$ $({\mu }_1=1)$ for air

${\mu }_2=\mu$

$\frac{\sin i}{\sin r}=\mu$

If ray emergence ll al

${60}^0+{90}^0+r={180}^0$

$r={30}^0$

$\frac{\sin {60}^0}{\sin {30}^0}=\mu$

$\frac{\sqrt{3}}{2}\times \frac{2}{1}=\mu$

$\mu =\sqrt{3}$