A ray of light is incident on a medium of refractive index ' $\mu$ ' at an angle of incidence ' $i$ ': On…

A ray of light is incident on a medium of refractive index ' $\mu$ ' at an angle of incidence ' $i$ ': On refraction in the medium ' $\delta$ ' is the angle of deviation. Then
  1. $\frac{1}{\mu}=\cos \delta-\frac{\sin \delta}{\tan i}$
  2. $\frac{1}{\mu}=\sin \delta-\frac{\cos \delta}{\tan i}$
  3. $\frac{1}{\mu}=\cos \delta-\sin \delta \cdot \tan i$
  4. $\frac{1}{\mu}=\sin \delta-\cos \delta \cdot \tan i$

Solution

$\begin{aligned} & \delta = \mathrm{i}+\mathrm{r} \\ \mu & =\frac{\sin i}{\sin r} \\ \therefore \quad \mu & =\frac{\sin i}{\sin (i-\delta)} \\ \therefore \quad \frac{1}{\mu} & =\frac{\sin (i-\delta)}{\sin i}=\frac{\sin i \cos \delta-\cos i \sin \delta}{\sin i} \\ \frac{1}{\mu} & =\cos \delta-\frac{\sin \delta}{\tan i}\end{aligned}$ .

Asked in: MHT CET 2024 (10 May Shift 1)

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