If refractive index of water is $\frac{4}{3}$ and that of a given glass slab immersed in it is $\frac{5}{3}$…

If refractive index of water is $\frac{4}{3}$ and that of a given glass slab immersed in it is $\frac{5}{3}$. The value of critical angle for a ray of light tending to go from glass to water is
  1. $\sin ^{-1}\left(\frac{4}{5}\right)$
  2. $\sin ^{-1}\left(\frac{3}{4}\right)$
  3. $\sin ^{-1}\left(\frac{5}{3}\right)$
  4. $\sin ^{-1}\left(\frac{4}{3}\right)$

Solution

Given, refractive index of water, ${ }_w \mu_a=4 / 3$ Refractive index of glass slab, ${ }_g \mu_a=5 / 3$ Refractive index of combined media $ \begin{aligned} & =\frac{g \mu_a}{{ }_w \mu_a}=\frac{5}{3} \times \frac{3}{4} \\ \Rightarrow \quad \mu & =\frac{5}{4} \end{aligned} $ Critical angle, $C=\sin ^{-1}\left(\frac{1}{\text { refractive index }}\right)$ $ \Rightarrow \quad C=\sin ^{-1}\left(\frac{4}{5}\right) $

Asked in: AP EAMCET 2021 (25 Aug Shift 2)

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