$\text{Apparent depth of water } d_A = d_R \frac{\mu_1}{\mu_2}$

$\text{Rate of change od apparent depth} \frac{\Delta d_A}{\Delta t} = \frac{\Delta d_R}{\Delta t}\frac{\mu_1}{\mu_2}$

$\frac{\Delta d_R}{\Delta t} = \frac{\Delta V}{\Delta t}$

$\Rightarrow  \frac{\Delta d_A}{\Delta t} = \frac{\Delta V}{\Delta t}\frac{\mu_1}{\mu_2}= \pi R^2 x \frac{\mu_1}{\mu_2}$