Light is incident from a medium A to medium B. The graph of sine of angle of incidence i versus sine of angle of refraction r is shown in fig. which of the following is/are correct ?

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Total internal reflection will not occur for any value of i

Total internal reflection occurs above a certain value of i

Wavelength of light in medium B is $\sqrt{3}$ times that in medium A.

Wavelength of light in medium B is $1 / \sqrt{3}$ times that in medium A.

answer is A, C.

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Detailed Solution

$μ_{A} \sin i = μ_{B} S i n_{r} \frac{μ_{A}}{μ_{B}} = \frac{S i n_{r}}{S i n_{i}} = \frac{0.433}{0.25} \frac{μ_{A}}{μ_{B}} = \sqrt{3} μ_{A} = \sqrt{3} μ_{B} ∴ T o t a l i n t e r n a l R e f l e c t i o n I s p o s s i b l e . μ_{A} = \sqrt{3} μ_{B} λ \propto \frac{1}{μ} λ_{A} \propto \frac{1}{μ_{A}} λ_{B} \propto \frac{1}{μ_{B}} \Rightarrow \frac{λ_{A}}{λ_{B}} \frac{μ_{B}}{μ_{A}} = \frac{μ_{B}}{\sqrt{3} μ_{B}} = \frac{1}{\sqrt{3}}$