First slide

Prism

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

Moderate

Solution

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

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