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

Answer 1

Answer: (B)

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 Eq.(i))]
$\Rightarrow \sin r=\frac{1}{{\mu }^2}$
$r={\sin }^{-1}\left(\frac{1}{{\mu }^2}\right)$