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A ray of light travelling in air in inci...

A ray of light travelling in air in inciden tat grazing angle (inciden angle `=90^@`) on a long rectangular slab of a tranparent medium of thickness`t=1.0m` . The point of incidence is the origin `A(0,0) .` The medium has a variable of refraction `n(y)` given by
`n(y)=[ky^(3//2)+1]^(1//2)`
where`k=1.0(m)^(-3//2)`
The refractive index of air is 1.0.
a. Obtain a relation between the slop of the trajectory of the ray at point `B(x,y)` in the medium and the incident angle at the point.
b. Obtain an equation for the trajectory `y(x)` of the ray in the medium.
c. Determing the coordinates `(x_(1),y_(1) )` of point P, where the ray intersects the upper surface of the slab-air boundary.
d. Indicate the path of the ray subsequently.

Text Solution

Verified by Experts

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