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Proving Fermat's principle using calculus

  1. Oct 9, 2007 #1
    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.
     
  2. jcsd
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