Hint: The deviation of light depends on the refractive index of the mixture.

Step 1: Use Snell's law.

Let us consider a portion of a ray between x and x+dx inside the liquid. Let the angle of incidence at x be $\mathrm{\theta }$ and let it enter the thin column at height y. Because of the bending, it shall emerge at x+dx with an angle $\mathrm{\theta }$+d$\mathrm{\theta }$ at a height y+dy.

From Snell's law,
or                  $\mathrm{\mu }\left(\mathrm{y}\right) \sin \mathrm{\theta }=\mathrm{\mu }\left(\mathrm{y}\right)\left(\mathrm{y}+\mathrm{dy}\right)\sin \left(\mathrm{\theta }+\mathrm{d\theta }\right)=\left(\mathrm{\mu }\left(\mathrm{y}\right)+\frac{\mathrm{d\mu }}{\mathrm{dy}}\mathrm{dy}\right)(\mathrm{sin\theta } \mathrm{cosd\theta }+\mathrm{cos\theta } \mathrm{sind\theta })$

As $\mathrm{d\theta } \mathrm{is} \mathrm{small}, \mathrm{cosd\theta }=1 \mathrm{and} \mathrm{sind\theta }=\mathrm{d\theta },$
or                               $\mathrm{\mu }\left(\mathrm{y}\right)\sin \mathrm{\theta }=\mathrm{\mu }\left(\mathrm{y}\right) \mathrm{cos\theta d\theta }+\frac{\mathrm{d\mu }}{\mathrm{dy}}\mathrm{dysin\theta }$
or                                       $\mathrm{\mu }\left(\mathrm{y}\right) \mathrm{cos\theta d\theta }=\frac{-\mathrm{d\mu }}{\mathrm{dy}}\mathrm{dy} \mathrm{sin\theta }$
                                                     $\mathrm{d\theta }=\frac{-\mathrm{d\mu }}{\mathrm{\mu dy}}\mathrm{dy} \mathrm{tan\theta }$
But                                                  $\mathrm{tan\theta }=\frac{\mathrm{dx}}{\mathrm{dy}}$                                 (from the figure)
On solving, we have
$\therefore$                                                  $\mathrm{d\theta }= \frac{-1 \mathrm{d\mu }}{\mathrm{\mu } \mathrm{dy}}\mathrm{dx}$

Step 2: Solve this differential equation.
Solving this variable separable form of a differential equation,
$\therefore$                                                  $\mathrm{\theta }= \frac{-1}{\mathrm{\mu } }\frac{ \mathrm{d\mu }}{\mathrm{dy}}{\int }_0^{\mathrm{d}}\mathrm{dx}=\frac{-1}{\mathrm{\mu } }\frac{ \mathrm{d\mu }}{\mathrm{dy}}\mathrm{d}$