Two transparent media A and B are separated by a plane boundary. The speed of light in those media are and respectively. The critical angle for a ray of light for these two media is [2022]

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Solution

Q.
Two transparent media A and B are separated by a plane boundary. The speed of light in those media are $1.5 \times 10^{8} m/s$ and $2.0 \times 10^{8} m/s$ respectively. The critical angle for a ray of light for these two media is [2022]

1 $\sin^{- 1} (0.500)$

2 $\sin^{- 1} (0.750)$

3 $\tan^{- 1} (0.500)$

4 $\tan^{- 1} (0.750)$

Ans.
(2)

For medium A, speed of light $v_{A} = 1.5 \times 10^{8} m/s$

For medium B, speed of light $v_{B} = 2.0 \times 10^{8} m/s$

For medium A, $n_{A} = \frac{c}{v_{A}} = \frac{3 \times 10^{8}}{1.5 \times 10^{8}} = 2$

For medium B, $n_{B} = \frac{c}{v_{B}} = \frac{3 \times 10^{8}}{2 \times 10^{8}} = 1.5$

The critical angle for a ray of light is,

$\sin C = \frac{n_{B}}{n_{A}}; C = \sin^{- 1} (\frac{1.5}{2}); C = \sin^{- 1} (0.750)$

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