A ray of light travelling in air is incident at angle of incidence I ≈ 90° on a long rectangular slab of a transparent medium of thickness y₀. The medium has a variable refractive index of $\mathrm{\mu }\left(\mathrm{x}\right)=\sqrt{1+{\mathrm{e}}^{2\mathrm{x}/\mathrm{a}}};\mathrm{x}\ge 0$, where ‘a’ is a positive constant. If the value of y₀ = a/2, then

the co-ordinates of the point where the ray intersects the upper surface of the slab-air boundary are $\left[\frac{\mathrm{a}}{2}\ln 2,\frac{\mathrm{a}}{2}\right]$

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

the angle made by light ray with +ve x-axis, at the upper surface of slab air boundary, inside the medium is $\mathrm{\pi }/3$

the co-ordinates of the point where the ray intersects the upper surface of the slab-air boundary are $\left[\mathrm{aln}2,\frac{\mathrm{a}}{2}\right]$