(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let v1 be the velocity of light in air and v2 the velocity of light in water. According to Fermat's principle, a ray of light will travel from a point A in the air to a point B in the water by a path ACB that minimizes the time taken.

2. Relevant equations

@=angle

sin(@1)/sin(@2)=v1/v2

@1= the angle of incidence

@2= the angle of refraction

3. The attempt at a solution

What is known:

1.) v1 and v2 are constants

2.) horizontal distance from A to B are constants

3.) t=d/v

v=dt

derivative of velocity= (AC)t

if the distance from the water to A is x and the distance from the water to B is y and x and y are constants then

t=csc@1x/v1 +csc@2y/v2

using this equation and the known variables i am not sure where to go from here.

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# Homework Help: Proving Fermat's principle using calculus

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