Question

A ray of light incident normally on an isosceles right angled prism travels as shown in the 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

Answer: (A)

From figure it is clear that TIR takes place at surface $A C$ and $B C$
i.e., $45^{\circ} > C$

$\Rightarrow \sin 45^{\circ}>\sin C $
$\Rightarrow \frac{1}{\sqrt{2}}>\frac{1}{\mu} \Rightarrow \mu>\sqrt{2}$
$\Rightarrow \mu>\sqrt{2}$
Hence $\mu_{\text {least }}=\sqrt{2}$