The velocity of light in transparent media A and B separated by a plane boundary are 2.0 $\times$ 108 and 2.5 $\times$ 108 ms−1 respectively. The critical angle for a light ray passing from A to B at the boundary is ______.

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KollegeApply · Accepted Answer

The critical angle for a light ray passing from A to B at the boundary is bbunderline(sin^-1 ($\frac{4}{5}$)). Explanation: Given: Velocity of light in medium A (vA) = 2.0 $\times$ 108 m/s Velocity of light in medium B (vB) = 2.5 $\times$ 108 m/s Light is going from medium A to B. Step 1: Refractive index: Refractive index nnn is inversely proportional to the speed of light in the medium: n_B/n_A = v_A/v_B = (2.0 xx 10^8)/(2.5 xx 10^8) = $\frac{2}{2}$.5 = $\frac{4}{5}$ Step 2: Critical angle formula: Critical angle $\theta$c​ (from denser to rarer): sin $\theta$_c = n_B/n_A sin $\theta$_c = $\frac{4}{5}$ $\theta$_c = sin^-1 ($\frac{4}{5}$)

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