Question

Glass has refractive index $\mu$ with respect to air and the critical angle for a ray of light going from glass to air is $\theta$. If a ray of light is incident from air on the glass with angle of incidence $\theta$, the corresponding angle of refraction is

• A. $\sin ^{-1}\left(\frac{1}{\sqrt{\mu}}\right)$
• B. $90^{\circ}$
• C. $\sin ^{-1}\left(\frac{1}{\mu^{2}}\right)$
• D. $\sin ^{-1}\left(\frac{1}{\mu}\right)$

Answer 1

Answer: (C)

${ }_{a} \mu_{g}=\frac{1}{\sin \theta}$
$ \Rightarrow \mu=\frac{1}{\sin \theta} ...$(i)
Now from Snell's law $\mu=\frac{\sin i}{\sin r}=\frac{\sin \theta}{\sin r}$
$\Rightarrow \sin r=\frac{\sin \theta}{\mu} \quad$.....(ii)
From equations (i) and (ii)
$\sin r=\frac{1}{\mu^{2}} $
$\Rightarrow r=\sin ^{-1}\left(\frac{1}{\mu^{2}}\right)$