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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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closed as off-topic by NowIGetToLearnWhatAHeadIs, user36790, Kyle Kanos, ACuriousMind, Qmechanic Oct 3 at 18:56

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1 Answer 1

Just use snell's law, that is, $\mu \,\sin\theta$=constant, where $\mu$ denotes the refractive index and $\theta$ is the angle between the ray and the normal between a generic point and the point of incidence.The rest is math, you need to express $\sin\theta$ in terms of the slope at that point and solve the resulting differential equation.

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