Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media A and B are 2.4 × 10⁸ m/s and 2.7 × 10⁸ m/s respectively, then the value of critical angle is :
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Question

Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media A and B are 2.4 × 10⁸ m/s and 2.7 × 10⁸ m/s respectively, then the value of critical angle is :

Options

G1 Physics · Accepted Answer

At the critical angle c for light travelling from denser medium A to rarer medium B, μ(A) sin c = μ(B). Therefore, sin c = μ(B)/μ(A). Since refractive index is inversely proportional to wave speed, μ(B)/μ(A) = v(A)/v(B). Hence, sin c = (2.4 × 10⁸)/(2.7 × 10⁸) = 8/9. Now, cos c = √[1 - (8/9)²] = √(17/81) = √17/9. Therefore, tan c = (8/9)/(√17/9) = 8/√17. Thus, c = tan⁻¹(8/√17). Correct option: C.