Question

A little kid stands at the edge of a wishing well of diameter 1.2 m, and shines a laser pointer (from a height of 0.8 m) into the well, trying to light up a quarter at the center of the bottom of the well. If the well is a cylinder 2.1 meters deep and half-full of water, at what distance from the side of the well should the light strike the surface of the water in order to illuminate the quarter?

Answer 1

Let i be the angle of incidence of the light at the surface of water and r be the angle of refraction.

Let x be the distance from the edge of the well at which point the light is incident on the water surface.

Then . Also we have . Here the term 1.05 m is half the height of the well.

From the law of refraction we have .

Therefore we have .

Putting y=0.6-x and simplifying the above equation we obtain

.

This is a quartic equation in y which must be solved to obtain y and hence x.