Question

Calculate the angle of incidence of the light ray incident on a surface of a plastic slab of refractive index $\sqrt{3}$, if the angle of refraction is ${30}^o$.

(Use: $sin{30}^o=\frac{1}{2}$ and $sin{60}^o=\frac{\sqrt{3}}{2}$)

Answer 1

Given: Light is travelling from air medium to the plastic slab

The angle of refraction $r={30}^o$

Refractive index of the plastic slab $n_2=\sqrt{3}$

Refractive index of air $n_1=1$

The angle of incidence $i=?$

Using Snell's law -

$n_{1}sini=n_{2}sinr$

$\Rightarrow sini=\frac{n_{2}sinr}{n_1}=\frac{\sqrt{3}\times sin{30}^o}{1}=\frac{\sqrt{3}}{2}=sin{60}^o$

$\Rightarrow i={60}^o$