Question

Refractive index of a prism is $\sqrt{7/3}$ and the angle of prism is ${60}^{\circ }$. The minimum angle of incidence of a ray that will be transmitted through the prism is

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${15}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is A ${30}^{\circ }$

A ray is projected on face LM of the prism gets refracted from the two faces of the prism and finally emerges out of it.

For minimum $i$, the emergent ray must graze on the face LN i-e. $e={90}^o$

Using Snell's law for face LN, $n_{2}sin{r}_2=n_{1}sine$

$\sqrt{\frac{7}{3}}sin{r}_2=1\times sin{90}^o$

This gives $r_2={40.89}^o$

As $A=r_1+r_2$ ,$A={60}^o$

$r_2={19.11}^o$

Using snell's law for face LN, $1\times sini=\sqrt{\frac{7}{3}}\times sin{19.11}^o$

This gives $i={30}^o$