Fermat’s Principle of Least Time

What is fermat’s principle?

This principle states that the light always travels that path in a medium from one point to another point which takes the minimum (i.e least) time.

Fermat’s Principle of Least Time

Consider a medium of refractive index n. The time taken by light ray to travel a distance dS in the medium is given by,

The total time taken by light ray to travel the path AB along the curve I is given by

Now let t’ be the time taken by light ray to travel path AB along the curve II. If path AB along the curve I is the actual path of ray of light, then t will be either equal or greater or less than t’ for any path AB along any curve like II.

Hence, according to Fermat’s principle, ray of light would follow that path put of many paths joining two points like A and B for which the time taken is minimum. Since c (speed of light) is constant, so the ray of light would follow a path for which

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