Question

derived fermat principle from laws of refraction for spherical surface

Answer 1

YOUR ANSWER IS:-

Fermat's Principle: Light follows the path of least time. Of course the straight line from A to B is the shortest time, but suppose it has a single reflection. The law of reflection can be derived from this principle as follows:

T he pathlength from A to B is

L=√a²+x²+√b²+[d-x]²

Since the speed is constant, the minimum time path is simply the minimum distance path. This may be found by setting the derivative of L with respect to x equal to zero.

dL/dx=1/2 2x/√a²+x²+1/2 2[d-x][-1]/2√b²+[d-x]²=0 {⊕ it means thitha}

This reduces to x/√a²+x²=[d-x]/√b²+[d-x]² which is sin⊕i=sin⊕r

⊕i=⊕r Law of refraction

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