JEE MAIN - Physics (2022 - 26th July Evening Shift - No. 7)
Light travels in two media $$M_{1}$$ and $$M_{2}$$ with speeds $$1.5 \times 10^{8} \mathrm{~ms}^{-1}$$ and $$2.0 \times 10^{8} \mathrm{~ms}^{-1}$$ respectively. The critical angle between them is :
$$\tan ^{-1}\left(\frac{3}{\sqrt{7}}\right)$$
$$\tan ^{-1}\left(\frac{2}{3}\right)$$
$$\cos ^{-1}\left(\frac{3}{4}\right)$$
$$\sin ^{-1}\left(\frac{2}{3}\right)$$
Explanation
Critical angle between them
$$\sin {i_c} = {{{\mu _2}} \over {{\mu _1}}} = {{{v_1}} \over {{v_2}}}$$
$$\sin {i_c} = {3 \over 4}$$
$$ \Rightarrow \tan {i_c} = {3 \over {\sqrt 7 }}$$
$${i_c} = {\tan ^{ - 1}}{3 \over {\sqrt 7 }}$$
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