A ray of light travelling in air is incident at grazing incidence on a slab with variable refractive index, $n\left(y\right)=[k{y}^{\frac{3}{2}} +1{]}^{\frac{1}{2}}$ where $k=1 {\mathrm{m}}^{\frac{-3}{2}}$ and follows the path as shown in the figure. What is the total deviation produced by the slab when the ray comes out? 

A beam of light is converging towards a point. A plane parallel plate of glass of thickness $t$, the refractive index $\mu$ is introduced in the path of the beam as shown in the figure. The convergent point is shifted by (assume near-normal incidence): 

Given that, the velocity of light in quartz is $1.5 \times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}$ and velocity of light in glycerine is $\left(\frac{9}{4}\right) \times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}.$ Now a slab made of quartz is placed in glycerine as shown. The shift of the object produced by the slab is 

A rectangular metal tank filled with a certain liquid is as shown in the figure. The observer, whose eye is in level with the top of the tank can just see the corner $E$ of the tank. Therefore, the minimum refractive index of the liquid is