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NEET PHYSICSMedium

Two transparent media A and B are separated by a plane boundary. The speed of light in those media are 1.5×1081.5 \times 10^8 m/s and 2.0×1082.0 \times 10^8 m/s, respectively. The critical angle for a ray of light for these two media is

A

sin⁡−1(0.500)\sin^{-1}(0.500)

B

sin⁡−1(0.750)\sin^{-1}(0.750)

C

tan⁡−1(0.500)\tan^{-1}(0.500)

D

tan⁡−1(0.750)\tan^{-1}(0.750)

Step-by-Step Solution

Refractive index of A, μA=3×1081.5×108=2\mu_A = \frac{3 \times 10^8}{1.5 \times 10^8} = 2. Refractive index of B, μB=3×1082×108=1.5\mu_B = \frac{3 \times 10^8}{2 \times 10^8} = 1.5. For Total Internal Reflection (TIR), ray of light should travel from denser to rarer medium. μAsin⁡θc=μBsin⁡90∘\mu_A \sin \theta_c = \mu_B \sin 90^{\circ}. 2sin⁡θc=1.5×12 \sin \theta_c = 1.5 \times 1. sin⁡θc=0.75\sin \theta_c = 0.75. θc=sin⁡−1(0.75)\theta_c = \sin^{-1}(0.75).

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