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Path Followed by a Light Ray

Problem Statement
Find the path followed by a light ray if the index of refraction (in polar coordinates) is proportional to r^-2.
Relevant Equations
∫nds
This is an example from a textbook. They show the following:

∫nds = ∫r-2*ds = ∫r-2*√((dr)2+r2*(dθ)2)

How do you obtain the expression for ds?
 
The arc length in Cartesian coordinate is given by :

##ds^2 = dx^2 + dy^2##
Which is Pythagoras theorem for an infinitesimal part of curve.

The transformation function to polar coordinate has form:

## x= r cos\theta##
##y=r sin\theta##


Substituting in above equation and manipulating gives desired result.
 
Got it! Thank you for your help.
 

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