Final answer:
The fraction of light from a point source in water that will escape through the surface can be found using the critical angle and geometrical optics, with the fraction being 1/2(1 - cos(critical angle)).
Step-by-step explanation:
To determine the fraction of light that will escape through the surface of the water, one must consider the critical angle and total internal reflection. The critical angle is the angle of incidence above which all light is reflected and none refracts out into the air. For water with a refractive index of 1.33, this angle is about 48.6°. Thus, light rays hitting the water-air interface at angles less than this will escape the water.
However, since this is a point source, light will be emitted in all directions, and only the rays that approach the surface within the critical angle range will refract out. The fraction can be found by considering the surface of a hemisphere (since light propagates spherically in the water). Rays pointing upwards within a cone defined by the critical angle will escape the water. Using solid angle concepts, the fraction is the ratio of the solid angle of the cone to that of the entire hemisphere: (2π(1 - cos(critical angle)))/(4π) which simplifies to 1/2(1 - cos(critical angle)).
Plugging in the known critical angle for water gives us the fraction of light that will escape, as not all rays are within this conical region. This is a geometrical optics consideration and assumes an ideal scenario with no absorption or scattering of light within the water.