A ray of light travelling in air is incident at grazing angle (incident angle=`90^(@))` on a long rectangular slab of a transparent medium of thickness `t=1.0` (see figure). The point of incidence is the origin `A(O,O)` .The medium has a variable index of refraction n(y) given by :`n(y)=[ky^(3//2)+1]^(1//2)` ,where k=`1.0m^(-3//2)`.the refractive index of air is 1.0`

(i) Obtain a relation between the slope of the trajectory of the ray at a point `B(x,y)`in the medium and the incident angle at that point
(ii) obtain an equation for the trajectory `y(x)`of the ray in the medium.
(ii) Determine the coordinates (`x_(1),y_(1))` of the point `P`.where the ray the ray intersects upper surface of the slab -air boundary.
Indicate the path of the ray subsequently.

Explanation

`m = y^((3)/(4))` (b) `4y^((1)/(4)) = x` (c) (4, 1)