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 $\mu =\frac{\sin i}{\sin r}=\frac{\sin \theta }{\sin r}$
$\Rightarrow \sin r=\frac{\sin \theta }{\mu }$.....(ii)
From equations (i) and (ii)
$\sin r=\frac{1}{{\mu }^2}$
$\Rightarrow r={\sin }^{-1}\left(\frac{1}{{\mu }^2}\right)$