The angle of incidence is found to be twice the angle of refraction when ray of light passes from vacuum…

The angle of incidence is found to be twice the angle of refraction when ray of light passes from vacuum into a medium of refractive index ' $\mu$ '. The angle of incidence will be
  1. $\cos ^{-1}\left(\frac{\mu}{2}\right)$
  2. $2 \cos ^{-1}\left(\frac{\mu}{2}\right)$
  3. $\sin ^{-1}\left(\frac{\mu}{2}\right)$
  4. $\quad 2 \sin ^{-1}\left(\frac{\mu}{2}\right)$

Solution

Snell's law, $\mu=\frac{\sin i}{\sin r}$ Given: $\mathrm{i}=2 \mathrm{r}$ $\begin{aligned} \therefore \quad r & =\frac{i}{2} \\ & \mu=\frac{\sin i}{\sin \left(\frac{i}{2}\right)} \\ & \mu=\frac{2 \sin \left(\frac{i}{2}\right) \cos \left(\frac{i}{2}\right)}{\sin \left(\frac{i}{2}\right)} \\ \therefore \quad & \mu=2 \cos \left(\frac{i}{2}\right) \end{aligned}$ $\Rightarrow i=2 \cos ^{-1}\left(\frac{\mu}{2}\right)$ .

Asked in: MHT CET 2024 (16 May Shift 1)

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