A glass prism ABC of refractive index 1.6 is immersed in a liquid as shown in Fig. A ray of light incident normally on face AB is totally reflected at face AC if the refractive of the liquid is

The ray falling normally on face AB goes into the prism undeviated and is incident on face AC at an angle i = $\theta$ = 45°. If μ₁ is the refractive index of the liquid, the ray incident on AC will be totally reflected if

$$\begin{gathered} \sin \mathrm{\theta }\ge \frac{{\mathrm{\mu }}_{\mathrm{l}}}{{\mathrm{\mu }}_{\mathrm{g}}} \\ \Rightarrow {\mathrm{\mu }}_{\mathrm{l}}\le {\mathrm{\mu }}_{\mathrm{g}} \sin \mathrm{\theta } \\ \Rightarrow {\mathrm{\mu }}_{\mathrm{l}}\le 1.6 \sin 45° \\ \Rightarrow {\mathrm{\mu }}_{\mathrm{l}}\le 0.8\sqrt{2} \end{gathered}$$