The refractive index of glass is $\frac{3}{2}$ and that of water is $\frac{4}{3}$. The critical angle for a…

The refractive index of glass is $\frac{3}{2}$ and that of water is $\frac{4}{3}$. The critical angle for a ray of light going from glass to water is
  1. $\sin ^{-1}\left(\frac{4}{7}\right)$
  2. $\sin ^{-1}\left(\frac{5}{8}\right)$
  3. $\sin ^{-1}\left(\frac{2}{3}\right)$
  4. $\sin ^{-1}\left(\frac{8}{9}\right)$

Solution

$\begin{aligned} \sin C &=\frac{1}{2 \mu_{1}} \\{ }_{2} \mu_{1} &=\frac{\mu_{1}}{\mu_{2}}=\frac{3 / 2}{4 / 3}=\frac{3}{2} \times \frac{3}{4}=\frac{9}{8} \\ \sin C &=\frac{1}{9 / 8}=\frac{8}{9} \\ \therefore C &=\sin ^{-1} \frac{8}{9} \end{aligned}$

Asked in: MHT CET 2020 (13 Oct Shift 1)

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