Probem63+Hannah+W.+Sharon,+Marlee

Yes, I am still working on this one as well! I am glad that it is in so many good hands!

#63

Let v1 be the volocity 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. Show that sinØ1/sinØ2 = v1/v2 where Ø1 (the angle of incidence) and Ø2 (the angle of refraction) are as shown. This equation is known as snell's law.

 To be honest, I really don't understand the physics behind this problem and I'm not sure how to even go about trying to show this---sharon
 * sinØ1/sinØ2 = (x1/h1)/(x2/h2)

I have absolutely no understanding of physics and never did, HOWEVER i do know that we are trying to minimize time. I am going to go out on a limb and state that the objective function is as follows:

Minimize T = T(AC) + T(CB), where T(AC) = the time it takes for the light to travel along AC and T(BC) = the time it takes for the light to travel along BC.

therefore, T = AC / v1 + BC/v2, since time = distance / rate. Now...can we solve for AC and BC in terms of our angles?? take it from there and see what happens!