The refractive index of glass is 1.5 and that of water is 1.33 . The critical angle for a ray of light going…

The refractive index of glass is 1.5 and that of water is 1.33 . 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. $\sin ^{-1}\left(\frac{8}{9}\right)$
  4. $\sin ^{-1}\left(\frac{2}{3}\right)$

Solution

$\begin{aligned} & \mu_{\mathrm{g}}=1.5=\frac{3}{2} \quad \mu_{\mathrm{w}}=1.33=\frac{4}{3} \\ & \therefore{ }_{\mathrm{w}} \mu_{\mathrm{g}}=\frac{\mu_{\mathrm{g}}}{\mu_{\mathrm{w}}}=\frac{3}{2} \times \frac{3}{4}=\frac{9}{8} \\ & \sin C=\frac{1}{{ }_w \mu_{\mathrm{g}}}=\frac{8}{9} \\ & \therefore \mathrm{C}=\sin ^{-1}\left(\frac{8}{9}\right)\end{aligned}$

Asked in: MHT CET 2021 (21 Sep Shift 2)

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