Two transparent media A and B are separated by a plane boundary. The speed of light in those media a

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Question

Two transparent media A and B are separated by a plane boundary. The speed of light in those media are 1.5 × 10⁸ m/s and 2.0 × 10⁸ m/s, respectively. The critical angle for a ray of light for these two media is

Accepted Answer

Correct Answer: C - sin⁻¹(0.750)Step-by-step Solution:Refractive index of medium A: n_A = c/v_A = (3 × 10⁸)/(1.5 × 10⁸) = 2 (denser medium). Refractive index of medium B: n_B = c/v_B = (3 × 10⁸)/(2.0 × 10⁸) = 1.5 (rarer medium).Critical angle is defined for light going from denser to rarer medium: sin i_c = n_B/n_A = 1.5/2 = 0.75. Therefore i_c = sin⁻¹(0.75).Why other options are incorrect: Options A and D use tan⁻¹, which is incorrect for the critical angle formula. Option B gives sin⁻¹(0.5) = 30°, which would require n_B/n_A = 0.5, but the correct ratio is 0.75.Key Concept: Critical angle: sin i_c = n_rarer/n_denser = v_denser/v_rarer. Total internal reflection occurs for angles of incidence greater than the critical angle.

Two transparent media A and B are separated by a plane boundary. The speed of light in those media are 1.5 × 10⁸ m/s and 2.0 × 10⁸ m/s, respectively. The critical angle for a ray of light for these two media is

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Two transparent media A and B are separated by a plane boundary. The speed of light in those media are 1.5 × 10⁸ m/s and 2.0 × 10⁸ m/s, respectively. The critical angle for a ray of light for these two media is

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