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 $\theta$, corresponding angle of refraction is

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

Answer 1

Answer: (B)

$sin^{-1}\left(\frac{1}{\mu^{2}}\right)$

Answer 2

Refractive index of glass with respect to air $=\mu$ Critical angle $=\theta$
$\therefore \mu=\frac{1}{\sin \theta}$...(i)
When a ray of light incident from air on the glass with angle of incidence $\theta$. If $r$ be the angle of refraction, then by Snell's law,
$\mu=\frac{\sin \theta}{\sin r}$
$\Rightarrow \sin r =\frac{\sin \theta}{\mu}=\frac{1 / \mu}{\mu}$ [from E(i))]
$\Rightarrow \sin r =\frac{1}{\mu^{2}}$
$r =\sin ^{-1}\left(\frac{1}{\mu^{2}}\right)$