Question

If you were underwater and looked upwards you would see a “circle of light” pouring down to
your eyes from the water’s surface. The light inside this circle originated from above the water’s surface.
Light outside of this circle originated from below the water’s surface (and is therefore darker.) This
phenomenon is due to total internal reflection. Suppose you were to lay on the bottom of the shallow
end of a pool (with a depth of 1 m) and looked upwards. How large would the circle of light be?

Answer 1

When a ray of light passing from a denser medium (water) to rarer medium (air), at critical angle(C), the refracted ray passes through the surface of separation.Hence the man on the bottom of the pool can see a circle of light upto critical angle.

Refractive index of water n=1/sinC Where n=1.33

sinC=1/n=1/1.33=.752

C=sin-1(0.752)=48.7

That is critical angle for water=48.7

If the angle of incidence from water to air is greater than 48.7, the ray will reflect towars water. Hence the man on the bottom of the pool can see a circle of light upto critical angle 48.7.

From the OAB in the picture

tanC=r/h

Where r= radius of the circle of light pouring down to his eyes  

h=OA=depth of pool=1m

tanC=r/h

tan48.7=r/1=r

r=tan48.7=1.14m

That is the radius of circle=1.14m

Its area=r2=3.14x(1.14)2=4m2