Question

The maximum refractive index of a material, of a prism of apex angle ${90}^{\circ },$ for which light may be

• A. $\sqrt{3}$
• B. $1.5$
• C. $\sqrt{2}$
• D. None of these

Answer 1

The correct option is C $\sqrt{2}$

Given, apex angle $A={90}^{\circ }$

For a prism the apex angle can also be written as

$A=r_1+r_2$

For critical angle it can be written as

$r_1=r_2={\theta }_C$

$\therefore 2{\theta }_C={90}^{\circ }$

$\Rightarrow {\theta }_C={45}^{\circ }$

Again $\sin {\theta }_C=\frac{1}{\mu }$

$\mu =\frac{1}{\sin {\theta }_C}=\frac{1}{\sin {45}^{\circ }}=\sqrt{2}$

Hence the correct answer is option (C).