Question

A ray of light is incident normally on an isosceles right-angled prism, travels as shown in figure. The least value of the refractive index of the prism must be:

• A. $\sqrt{2}$
• B. $\sqrt{3}$
• C. $1.5$
• D. $2.0$

Answer 1

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

From figure it is clear that $TIR$ takes place at surface $AC$ and $BC$
i.e. ${45}^o>C$
$\Rightarrow \sin {45}^o>\sin C$
$\Rightarrow \frac{1}{\sqrt{2}}>\frac{1}{\mu }\Rightarrow \mu >\sqrt{2}$
Hence ${\mu }_{least}=\sqrt{2}$