The apparent depth of water in cylindrical water tank of diameter 2 R ~cm is reducing at the rate of x ~cm / minute when water is being drained out at a constant rate. The amount of water drained in c.c. per minute is ( n₁= refractive index of air, n₂= refractive index of water).

Step-by-step solution

n₂ n₁ = real depth apparent depth or, n₂ n₁ = h x Differentiating with respect to time, n₂ n₁ = d h / d t d x / d t Change in real depth = n₂ n₁ change in apparent depth d h d t = n₂ n₁ x ~cm / min The amount of water drained in c.c. per minute = d h d t R^2=x R^2 n₂ n₁ .