Question

A ray of light of pure single colour is incident on the face of a prism having angle of the prism ${30}^{\circ }$ at an angle of incidence ${45}^{\circ }$. The refracted ray does not change its direction as its crosses the other face and emerges out of the prism. The refractive index of the material of the prism is

• A. $\frac{2}{\sqrt{3}}$
• B. $2$
• C. $\sqrt{2}$
• D. $\sqrt{3}$

Answer 1

Answer: (C)

$\sqrt{2}$

For no derviation from Face $2$, it should pass normally from Face $-2$
We know that for a prism of Angle $A$ and $r_1$ and $r_2$ as refraction angles.
$A=r_1+r_2$
${30}^{\circ }=r_1+0^{\circ }$
$r_1={30}^{\circ }$
$\therefore$ By relation $\frac{\sin i_1}{\sin r_1}={\mu }_{21}\Rightarrow \frac{\sin {45}^{\circ }}{\sin {30}^{\circ }}={\mu }_{21}$
${\mu }_{21}=\sqrt{2}$.