Ray Optics

JEE Main level, single correct, medium

56 of 295

Question 56 of 295

Light travels in two media M1{M}_{1} and M2{M}_{2} with speeds 1.5×108ms−11.5\times {10}^{8}m{s}^{-1} and 2.0×108ms−12.0\times {10}^{8}m{s}^{-1} respectively. The critical angle between them is

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Answer: (A) tan⁡−1(37){\tan }^{-1}\left(\dfrac{3}{\sqrt{7}}\right)

Relative refractive index can be found as,
μ2μ1=v1v2=1.52=34\dfrac{{\mu }_{2}}{{\mu }_{1}}=\dfrac{{v}_{1}}{{v}_{2}}=\dfrac{1.5}{2}=\dfrac{3}{4}.
When the angle of incident is greater than the critical angle total internal reflection occurs. If the critical angle is ic{i}_{c} then,
sin⁡ic=μ2μ1=34\sin {i}_{c}=\dfrac{{\mu }_{2}}{{\mu }_{1}}=\dfrac{3}{4}
Now tan⁡ic=342−32=37\tan {i}_{c}=\dfrac{3}{\sqrt{{4}^{2}-{3}^{2}}}=\dfrac{3}{\sqrt{7}}
Therefore, ic=tan⁡−1(37){i}_{c}={\tan }^{-1}\left(\dfrac{3}{\sqrt{7}}\right)

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