Question

When a ray of light enters a medium of refractive index $\mu$ from air. It is observed that the angle of refraction is half the angle of incidence. The angle of incidence is :

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

Answer 1

The correct option is A $2co{s}^{-1}\left(\frac{\mu }{2}\right)$

$\text{r =}\frac{\text{i}}{2}$

Using Snell’s law,

$\mu =\frac{\text{sin i}}{\text{sin r}}$

Substituting the values,

$\mu =\frac{\text{sin i}}{\text{sin}\left(\frac{\text{i}}{2}\right)}$

$\mu =\frac{\text{2sin}\left(\frac{\text{i}}{2}\right)\text{cos}\left(\frac{\text{i}}{2}\right)}{\text{sin}\left(\frac{\text{i}}{2}\right)}$

$\frac{\mu }{2}=\text{cos}\left(\frac{\text{i}}{2}\right)$

$\frac{\text{i}}{2}=\text{co}{\text{s}}^{-1}\left(\frac{\mu }{2}\right)$

$\text{i}=\text{2co}{\text{s}}^{-1}\left(\frac{\mu }{2}\right)$