Question

A swimming pool appears to be 3.30 m deep when looking at an angle of incidence of 25 degrees, how deep is it really? n = 1.33  


My professor provided this as the answer: "Use the approximation that the x distance doesn't appear to change, just the y depth. This isn't completely true, but is a good approximation. That means our eyes believe the light doesn't bend. So we think the triangle below the surface still is at an angle of 25 degrees to the normal. by trigonometry, that gives the x distance of 1.538815 m. But in reality the light bends toward the normal, by snell's law, we get the refracted light at an angle of 18.527398 degrees. using the x distance equality approximation, by trig we get a y depth of 4.59 m."

However, I do not really understand what he did to get those values. If someone can please provide the worked out formulas I'd very much appreciate it.

Answer 1