Mike has installed a light bulb at the bottom of his water pool. At night, he turns on the light. He observes that the light produces a bright circle with a radius
of one meter on the water surface. The rest of the surface is completely dark.
The reason is that the rest of the light rays go under total internal reflection and
do not get out of the water. How deep is the pool? The refraction index of water
is n=1.3.

Arunner is jogging at a steady 3.6 km/hr. when the runner is 2.9 km from the finish line, a bird begins flying from the runner to the finish line at 14.4 km/hr (4 times as fast as the runner). when the bird reaches the finish line, it turns around and flies back to the runner. even though the bird is a dodo, we will assume that it occupies only one point in space, i.e., a zero-length bird. how far does the bird travel? (b) after this first encounter, the bird then turns around and flies from the runner back to the finish line, turns around again and flies back to the runner. the bird repeats the back and forth trips until the runner reaches the finish line. how far does the bird travel from the beginning? (i.e. include the distance traveled to the first encounter)