Wednesday, 17 August 2016

homework and exercises - Path of a light ray in a medium of varying refractive index



How do we get the equation for the path of a light ray in a medium of varying refractive index.


I can draw a rough sketch, but don't know how do we get the exact curve.



I encountered this while doing a problem:



A ray of light travelling in air makes a grazing incidence on a rectangular slab of transparent medium with one vertex at the origin & (sides along x and y axes.)



The refractive index of the material varies as $N=2x$. The path of the light ray is given by?


(The ray makes a grazing incidence nearly parallel to x axis from -ve to +ve x axis but just enough to enter the first quadrant; where the slab lies.)




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