Suppose a ray of light travels from (x,y) = (-1,1) to (x,y) = (1,1) in a region where the index of refraction is n(y) = e^y.
(a) Find the path.
The Attempt at a Solution
Is this okay?
The positions of the light ray are given by
initial (xi,yi) = (-1,1)
Final (xf,yf) = (+1,1)
Clearly the Y coordinate is invaiant
the refractive index of the region
n(y) = e^y
n(1) = e = 2.718
As the light ray travells, the index of refraction is invariant, so the ray will travell in straight line path from (xi,yi) to (xf,yf).