Physics
Physics
Problem
There is a small source of light at some depth below the surface of water (refractive index ) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly): [Use the fact that surface area of a spherical cap of height and radius of curvature is ] a. 21% b. 34% c. 17% d. 50%Intuitive explanation
The key here is total internal reflection: light from an underwater source can only escape through a cone-shaped region on the water surface, because rays hitting the surface at angles too steep to the normal will bounce back down. Find the critical angle where refraction just becomes impossible, then use it to determine what fraction of the light sphere actually escapes. The hint about spherical cap area lets you calculate the solid angle of the escape cone relative to the full sphere.
Intuitive explanation
The key here is total internal reflection: light from an underwater source can only escape through a cone-shaped region on the water surface, because rays hitting the surface at angles too steep to the normal will bounce back down. Find the critical angle where refraction just becomes impossible, then use it to determine what fraction of the light sphere actually escapes. The hint about spherical cap area lets you calculate the solid angle of the escape cone relative to the full sphere.