Question

A glass prism of refractive index 1.5 is immersed in water (refractive index $\frac{4}{3}$).A light beam incident normally on the face AB is totally reflected to reach on the face BC if

• A. $sin\theta$ >$\frac{8}{9}$
• B. $\frac{2}{3}$ < $sin\theta$< $\frac{8}{9}$
• C. $\frac{1}{2}$ < $sin\theta$ <$\frac{8}{9}$
• D. $\frac{1}{2}$ < $sin\theta$

Answer 1

The correct option is A $sin\theta$ >$\frac{8}{9}$

Total internal reflection occurs when the ray of light travels from
denser medium to rarer medium and the angle of incidence is
greater than the critical angle.
At P, glass is denser and water is rarer.

$g_{{\mu }_w}=\frac{g_{{\mu }_w}}{a_{{\mu }_g}}=\frac{\frac{4}{3}}{\frac{3}{2}}=\frac{8}{9}$
$\therefore sin{i}_c=\frac{8}{9}$ where $i_c$ = critical angle
$\therefore \theta$ > $i_c$ or $sin\theta =\frac{8}{9}$ for critical angle.
For total internal reflection, $sin\theta$ > $\frac{8}{9}$