Geometrical OpticsHard

Question

Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media $A$ and $B$ are $2.4 \times 10^{8}\text{ }m/s$ and $2.7 \times 10^{8}\text{ }m/s$ respectively, then the value of critical angle is :

Options

A.$\cot^{- 1}\left( \frac{3}{\sqrt{13}} \right)$
B.$\sin^{- 1}\left( \frac{9}{8} \right)$
C.$\tan^{- 1}\left( \frac{8}{\sqrt{17}} \right)$
D.$\cos^{- 1}\left( \frac{8}{9} \right)$

Solution

$${\mu_{A}sinc = \mu_{B}sin90 }{\Rightarrow sinc = \frac{\mu_{B}}{\mu_{A}} = \frac{v_{A}}{v_{B}} }{\therefore sinc = \frac{2.4 \times 10^{8}}{2.7 \times 10^{8}} = \frac{8}{9} }{\Rightarrow tanc = \frac{8}{\sqrt{81 - 64}} = \frac{8}{\sqrt{17}} }{c = \tan^{- 1}\left( \frac{8}{\sqrt{17}} \right)}$$

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