Math 1A Group Project Problem
by EpicSkills32, Jul 31, 2014, 5:13 AM
![$\ [\text{Blog Post 110}] $](http://latex.artofproblemsolving.com/4/6/f/46fdcb2187670aafc5e546f1ba6154b35443630d.png)
So I almost refrained from posting today...
A few days ago (I think Monday), I talked to thkim about what problem to do for our group project, and (after he solved one of two choices on the spot) I ended up picking the famous Snell's Law problem. If you've had calculus and optimization, you've probably seen it. This problem is in my textbook for this course, the textbook I used before, and the AoPS calculus textbook.
be the velocity of light in air and 
be 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![\[ \dfrac{\sin \theta_1}{\sin\theta_2}=\dfrac{v_1}{v_2} \]](http://latex.artofproblemsolving.com/7/3/8/738991b702d2d937ecd6a90466e9c78de9c27e29.png)
where 
(the angle of incidence) and 
(the angle of refraction) are as shown. This equation is known as Snell's Law.
I haven't actually tried solving it yet (planning to do that tomorrow), but after I do I'll have to make some slides and stuff to present it to the class.
lol this problem looks surprisingly like the one I was originally going to do for the project, but much simpler. oh well.
Ok so I got it. Too lazy to post the solution now, but I'm making slides for our project presentation so I might upload those later when they're done. In the meantime, where's thkim to help me on that...
but that dubstep tho.
This post has been edited 6 times. Last edited by EpicSkills32, Aug 3, 2014, 5:30 AM
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