a point source of light is 12cm below the surface of a large body of
water(n=1.33)what is the radius of the largest circle on the water
surface through which the light can emerge?

Radius of the lighted circle  Rl is

Rl = Depth * ctg alfa,

where Depth = 12 cm

alfa= critical angle, such alf that sin(alpha) = 1/n = .75

 Theory is at 
http://library.thinkquest.org/22915/refraction.html

SEARCH TERMS: snellius law, critical angle, total reflection

Note: ctg alfa is cotangent alfa =sqrt(1 -s *s) / s  = cos alfa / sin alfa 

where s = sin alfa = 3/4 

I do not see any fibers in this, but that would be the lighted circle
assuming the point source is isotropic (radiates in all directions).

Unfortunately, hedgie has given the wrong answer.

The critical angle (hedgie called it alpha) is indeed arcsin(1/n), but
the radius is depth * tan(alpha), not depth * ctg(alpha).

So, the correct answer is that the radius of the circle is 
12cm * tan(arcsin(1/1.33)) = 13.7 cm.

The formula given in the "Answer" gets you 10.5 cm.