The speed of light in media $\mathbf{M}_1$ and $\mathrm{M}_2$ is $1.5 \times 10^8 \mathrm{~m} / \mathrm{s}$…

The speed of light in media $\mathbf{M}_1$ and $\mathrm{M}_2$ is $1.5 \times 10^8 \mathrm{~m} / \mathrm{s}$ and $2.0 \times 10^8 \mathrm{~m} / \mathrm{s}$ respectively. A ray of light enters from medium $\mathrm{M}_1$ to $\mathrm{M}_2$ at an incidence angle $i$. If the ray suffers total internal reflection, the value of $i$ is
  1. equal to $\sin ^{-1}\left(\frac{2}{3}\right)$
  2. equal to or less than $\sin ^{-1}\left(\frac{3}{5}\right)$
  3. equal to or greater than $\sin ^{-1}\left(\frac{3}{4}\right)$
  4. less than $\sin ^{-1}\left(\frac{2}{3}\right)$

Solution

In total internal reflection, the angle of incidence (i) must be greater than critical angle $C$ $\because \quad \begin{aligned} 2 \mu_1 & =2 \text { and } \mu_2=\frac{3}{2} \\ 2 \sin \mathrm{i} & \geq \frac{3}{2} \sin 90^{\circ} \\ \sin \mathrm{i} & \geq \frac{3}{4} \\ \mathrm{i} & \geq \sin ^{-1}\left(\frac{3}{4}\right) \end{aligned}$

Asked in: NEET 2010 (Mains)

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