Ray Optics

JEE Main level, single correct, medium

57 of 295

Question 57 of 295

The speed of light in media ′A′'A' and ′B′'B' are 2.0×1010cms−12.0\times {10}^{10}cm{s}^{-1} and 1.5×1010cms−11.5\times {10}^{10}cm{s}^{-1} respectively. A ray of light enters from the medium BB to AA at an incident angle′θ′'\theta '. If the ray suffers total internal reflection, then

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Answer: (C) θ>sin⁡−1(34)\theta \gt {\sin }^{-1}\left(\dfrac{3}{4}\right)

Given:vA=2×108ms−1{v}_{A}=2\times {10}^{8}m{s}^{-1} and vB=1.5×108ms−1{v}_{B}=1.5\times {10}^{8}m{s}^{-1}
For critical angle:sin⁡(θc)=μAμB=cvA×vBc=1.5×1082×108=34\sin \left({\theta }_{c}\right)=\dfrac{{\mu }_{A}}{{\mu }_{B}}=\dfrac{c}{{v}_{A}}\times \dfrac{{v}_{B}}{c}=\dfrac{1.5\times {10}^{8}}{2\times {10}^{8}}=\dfrac{3}{4}
⇒θc=sin⁡−1(34)\Rightarrow {\theta }_{c}={\sin }^{-1}\left(\dfrac{3}{4}\right)
Now for TIR,θ>θCTIR,\theta \gt {\theta }_{C}
So, θc>sin⁡−1(34){\theta }_{c}\gt {\sin }^{-1}\left(\dfrac{3}{4}\right)

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