Light in Underwater Pool Refraction Problem

JSGandora

1. The problem statement, all variables and given/known data
A small underwater pool light is 1 meter below the surface of a swimming pool. What is the radius of the circle of light on the surface, from which light emerges from the water?
2. Relevant equations
Snell's Law
Fermat's Principle


3. The attempt at a solutionI have no idea about how to approach the first part because we're not given the radius of the light.

ehild

It is small. Consider it a point source of light. It will illuminate the surface: the light rays cross the water surface and arrive to the eyes of the observer. But not all rays can escape from the water: Find the angle where the rays incident on the surface of the water totally reflect. Make a drawing!

ehild

JSGandora

Ohh, thank you so much. It's just the critical angle, or 48.6 degrees, making the radius to be 1/tan(48.6)=1.13m.

ehild

It is correct.

ehild