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A, B and C are three optical media of respective critical angles $C_{1} {,C}_{2} {and C}_{3}$ . Total internal reflection of light can occur from A to B and also from B to C but not from C to A. Then the correct relation between critical angles is

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$C_{1} {> C}_{2} > C_{3}$

$C_{3} {> C}_{1} > C_{2}$

$C_{1} {< C}_{2} < C_{3}$

$C_{1} {= C}_{2} = C_{3}$

answer is D.

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Detailed Solution

A is denser than B and B is denser than C. $\sin C_{1} = \frac{1}{μ_{1}}, \sin C_{2} = \frac{1}{μ_{2}}, \sin C_{3} = \frac{1}{μ_{3}}$

We can have $\frac{1}{μ_{1}} < \frac{1}{μ_{2}} < \frac{1}{μ_{3}}$

$∴ μ_{1} > μ_{2} > μ_{3}$

$∴ C_{1} < C_{2} < C_{3}$

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