Question

A glass vessel in the shape of the triangular prism is filled with water, and light is incident normally on the face xy. If the refractive indices for water and glass are $\frac{4}{3}$ and $\frac{3}{2}$ respectively, total internal reflection will occur at the glass-air surface $xz$ only for $\sin \theta$ greater than

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{3}{4}$
• D. $\frac{8}{9}$

Answer 1

The correct option is C $\frac{3}{4}$

$\frac{\sin i}{\sin r}=\frac{ng}{nw}=\frac{3\times 3}{2\times 4}=\left(\frac{9}{8}\right)$
$\frac{\sin r}{\sin r_1}=\left(\frac{nair}{ng}\right)=\frac{1}{\left(\frac{3}{2}\right)}=\left(\frac{2}{3}\right)$
$\frac{\sin r}{\sin 90}=\frac{2}{3}\Rightarrow \sin r⩾\left(\frac{2}{3}\right)$
$\frac{8\sin i}{\sin 90}⩾9$
or
$\sin i⩾\frac{3}{4}$