Physics -Mirrors?

Question

A point source of light is submerged 3.0 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?

Answer 1

The critical angle for water is about 49 degrees, so the answer is:

r = 3 m * Tan(48.75) = 3.42 m

The critical angle can be found by the expression:

θ = ArcSin( 1/1.33 ) = 48.75°

where 1 is the index of refraction for air, and 1.33 is the index of refraction for water, and θ is the angle from the vertical.

Answer 2

critical angle theta = arcsin(n2/n1)

where n1,n2 are the refractive indexes of the media
refractive index of water is reputed to be 1.33

Google's built-in calculator shows
(180 / pi) * asin(1 / 1.33) = 48.7534666

(angle needs to be in radians so factor 180/pi is needed)
so scythian1's figure of 48.75 seems to be correct.

Google built in calculator
shows

3 * tan((pi / 180) * 48.75) = 3.42084437

radius is 3.42084437 metres

or simply
3*tan(asin(1/1.33))= 3.42126193


So agrees scythian1's answer 3.42m

(I cheated by checking with scythian1's answer)