Question

Obtain a relation between the slope $\left(dy/dx\right)$ of the trajectory of the ray at a point $B(x,y)$ in the medium and the incident angle ($l$) at that point.

Answer 1

Given that $\mu =[k{y}^{\frac{3}{2}}+1{]}^{\frac{1}{2}}$
Slope at a point P $=\frac{dy}{dx}$ $=\tan (90-\theta )$

$\frac{dy}{dx}$ $=\cot \theta$, hence $\theta$ is angle of incidence.