Question

A glass vessel in the shape of a triangular is filled with water, and light is incident normally on the face XY. If the refractive indices for water and glass are $4/3$ and $3/2$ respectively, total internal reflection will occur at the glass- air surface XY only. What is the minimum value of sin$\theta$

• A. $>\frac{2}{3}$
• B. $<\frac{2}{3}$
• C. $>\frac{4}{3}$
• D. $<\frac{4}{3}$

Answer 1

The correct option is A $>\frac{2}{3}$

$\mu =\frac{1}{\sin C}$ [ where u is the refractive index $\left(\frac{u_2}{u_1}\right)$ C is critical angle ]

$\Rightarrow \frac{u_2}{u_1}=\frac{1}{\sin C}$

$\Rightarrow \frac{\frac{3}{2}}{\frac{4}{3}}=\frac{1}{\sin C}$

$\Rightarrow \frac{3}{2}\times \frac{3}{4}=\frac{1}{\sin C}$

$\Rightarrow \frac{9}{8}=\frac{1}{\sin C}$

$\therefore \sin C=\frac{8}{9}$

$C=62.73°$ ( approx. )

Incident ray is perpendicular.

Therefore it would not show any refraction or reflection. When incident ray reaches AC.

It would make a $△$ with angle of prism ${60}^0$ and with $ac=180°60°+90°=30°$

Angle of incidence $=90°-30°=60°$

Since incident angle is less than critical angle.