An observer in a small boat is floating on the surface of a large lake with clear, but contaminated water with index of refraction n = 1.38. Nearby is a wooden post emerging from the water which is embedded in the lake bottom, a distance h = 7.20 meters below the water's surface. What is the maximum distance from the post at which the observer would be able to see the bottom of the post?

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anonymous · Answer

Hey i just had a problem like this: here is what i did... use snell's equation first to find the tetha of the second index of refraction (of the water)... hopefully this makes sense: 1.003sin(90)=1.38sin(theta) you must solve this equation for tetha. we get theta=sin ^-1(1.003*1/1.38)  That will give you theta = 46.6198 degrees. Now since you are trying to find the length of the hypotenuse (from the boat down to the bottom of the post) you need to solve 7.20tan(46.6198). Your answer should be 7.619 meters. :D