Question

A point source of light is submerged 2.0 m below the surface of a lake and emits rays in all directions. On the surface of the lake, directly above the source, the area illuminated is a circle. What is the maximum radius that this circle could have? Take the refraction index of water to be 1.333.

Answer 1

Answer:

The maximum radius that this circle is r=2.685m

Explanation:

The circle on the surface will exit the total reflection occurs

on the point the angle of reflection 90°

The critical angle for air water interface is:

$Sin\alpha =\frac{n_{2} }{n_{1}} \\Sin\alpha =\frac{1.00}{1.33}\\\alpha =Sin^{-1}(\frac{1.00}{1.33})\\\alpha =48.6^{o}$

The radius of circle on the surface is AO.From geometry

$tan\alpha =\frac{AO}{OS}\\ AO=tan\alpha (OS)\\r=tan(48.6)(2.0)\\r=2.685m$  

The maximum radius that this circle is r=2.685m