A ray of light travelling in air is incident at an angle of incidence $i\approx {90}^o$ on a long rectangular slab of a transparent medium of thickness $y_0.$ The medium has a variable  refractive index of $\mu \left(x\right)=\sqrt{1+e^{2x/a}}\forall x\ge 0,$ Where ‘a’ is a positive constant. Which of the following is/are correct?

 

If $y_0=a/2,$ the coordinates of the point where the ray intersects the upper surface of the slab- air boundary are $(a\mathcal{l}n2,a/2)$  

In the above situation if $y_0=a/2,$ the coordinates of the point where the ray intersects the upper surface of the slab- air boundary are $\left(\frac{a}{2}\mathcal{l}n2,a/2\right)$

If $y_0=\frac{a}{2},$ the angle made by light ray with +ve x-axis at the upper surface of slab –air interface, inside the medium is ${\tan }^{-1}\left(\frac{1}{2}\right)$

If $y_0=\frac{a}{2},$ the angle made by light ray with +ve x-axis at the upper surface of slab-air interface, inside the medium is ${\tan }^{-1}\left(2\right)$