Question

A ray of light propagates from glass (refractive index $=\frac{3}{2}$ ) to water (refractive index $\left.=\frac{4}{3}\right)$. The value of the critical angle is.

• A. $\sin ^{-1}\left(\frac{1}{2}\right)$
• B. $\sin ^{-1}\left(\sqrt{\frac{9}{8}}\right)$
• C. $\sin ^{-1}\left(\frac{8}{9}\right)$
• D. $\sin ^{-1}\left(\frac{5}{7}\right)$

Answer 1

Answer: (C)

The angle of incidence in denser medium for which the angle of refraction in rarer medium is $90^{\circ}$ is called the critical angle $(C)$.
$\mu_{w}$ and $\mu_{g}$ are refractive indices for rarer (water) and denser (glass) media, then
$\frac{\sin C}{\sin 90^{\circ}}=\frac{\mu_{w}}{\mu_{g}}$

$\Rightarrow \sin C=\frac{4 / 3}{3 / 2}=\frac{8}{9}$
$\Rightarrow C=\sin ^{-1}\left(\frac{8}{9}\right)$
Note : The critical angle for water-air, glass-air and diamond-air interfaces are $49^{\circ}, 42^{\circ}$ and $24^{\circ}$, respectively.