A light ray passes from air ( ) into water

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

A light ray passes from air (n1=1.00n_1 = 1.00) into water, where the refractive index n2n_2 changes slowly with temperature. At one instant θ1=30∘\theta_1 = 30^{\circ}, θ2=20∘\theta_2 = 20^{\circ}, and n2n_2 is increasing at 0.002 s−10.002\,\text{s}^{-1}. The angle θ1\theta_1 is increasing at 0.010 rad/s0.010\,\text{rad/s}. According to the law of refraction, what is the instantaneous rate of change of the angle of refraction, dθ2/dtd\theta_2/dt, at that instant? (a) +6.3×10−3 rad/s+6.3\times 10^{-3}\,\text{rad/s} (b) −5.8×10−3 rad/s-5.8\times 10^{-3}\,\text{rad/s} (c) +5.8×10−3 rad/s+5.8\times 10^{-3}\,\text{rad/s} (d) +4.2×10−3 rad/s+4.2\times 10^{-3}\,\text{rad/s}

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