Question

A trihedral with refracting angle ${60}^o$ deviates a light ray by ${30}^o$. the refractive index of the material of prism:

• A. may be equal to $\sqrt{2}$
• B. can not be greater than $\sqrt{2}$
• C. can not be less than $\sqrt{2}$
• D. none of these

Answer 1

The correct option is A may be equal to $\sqrt{2}$

$A={60}^{\circ },\delta ={30}^{\circ }$

$i=\frac{A+\delta }{2}=45$

$r=\frac{A}{2}=30$

$\frac{\sin i}{\sin r}=\frac{n_2}{n_1}$

$\frac{\sin 45}{\sin 30}=\frac{n_2}{1}$

$n_2=\sqrt{2}$