JEE PYQ: Wave Optics Question 30
Question 30 - 2019 (12 Apr Shift 2)
A transparent cube of side $d$, made of a material of refractive index $\mu_2$, is immersed in a liquid of refractive index $\mu_1$($\mu_1 < \mu_2$). A ray is incident on the face AB at an angle $\theta$ (shown in the figure). Total internal reflection takes place at point E on the face BC.
Then $\theta$ must satisfy :
(1) $\theta < \sin^{-1}\frac{\mu_1}{\mu_2}$
(2) $\theta > \sin^{-1}\sqrt{\frac{\mu_2^2}{\mu_1^2} - 1}$
(3) $\theta < \sin^{-1}\sqrt{\frac{\mu_2^2}{\mu_1^2} - 1}$
(4) $\theta > \sin^{-1}\frac{\mu_1}{\mu_2}$
Show Answer
Answer: (3)
Solution
Using, $\sin\theta_{\max} = \mu_1\sqrt{\frac{\mu_2^2}{\mu_1^2} - \mu_1^2} = \sqrt{\frac{\mu_2^2}{\mu_1^2} - 1}$
or $\theta_{\max} = \sin^{-1}\left(\sqrt{\frac{\mu_2^2}{\mu_1^2} - 1}\right)$
For T.R., $\theta < \sin^{-1}\left(\sqrt{\frac{\mu_2^2}{\mu_1^2} - 1}\right)$
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