Difficult problem?

[mrjust]

When you look down at an object under water the reason it appears to be in a different place than it really is to you is that light always travels along a path that minimizes the time of travel from the object to your eye. But light travels slower in water than in air. So the light comes out of the water at a different spot than the straight path to your eye, hence the illusion. in the drawing below you are 2 meters tall and standing in a 1 meter deep pond and the object is 5 meters away on the bottom as shown. Light travels at approx. 3*10^8 m/sec in the air and the water is very muddy so it travels 2.7*10^8 m/sec in the water. Find the value of x shown such that the time of travel of the light form the object to your eye is minimized. Hint: d=rt so t=d/t.

For the time above the water I got
t= (1+x^2)^.5/(3(10^8)
and for the time in the muddy water I got:
t= (1+(5-x)^2)^.5/(2.7(10^8))

I don't know where to go from here; I'm not sure if this is what I am supposed to do?

 

[MarkFL]

I posted a tutorial topic at MHB on the application of Snell's law which you might find helpful:

http://www.mathhelpboards.com/f49/using-snells-law-determine-fastest-escape-route-4178/

 

[mrjust]

I have solved it. I started correct with the two function I have in the first post. From their all I had to do was take the sum of the total time( Ttotal= time1+time2) , take the derivative set it to zero and graph it. Once I found the root I pluged it into my Time function and saw that in fact the x value that I derived from the first derivative minized the time.