I was on a mini-vacation this past weekend, escaping the DC heat by going to a place that was only slightly less miserable (~95ºF instead of 100ºF) but I did have the benefit of a pool in which to do a little physics demonstration.
That’s me (I’m the one in the “Make it look like an accident”/Humpty was pushed t-shirt) waterboarding my camera. I set my GOPRO (in its waterproof case) to the time-lapse setting rather than the timer so it would take the pictures automatically as I immersed and panned it, and I wouldn’t have to keep disturbing the water’s surface to reset anything.
What you are seeing here is an effect called Snell’s Circle or Snell’s Window: the light from outside the pool refracts as it enters, and this bending means that the entire view of the outside is compressed into a cone.
Snell’s law tells us that
\(n_1sintheta_1 = n_2sintheta_2\)
Water has an index of refraction of 4/3, so light with a grazing incidence to the water (n=1 for air, and sin(90º)=1) will be bent to about 38.5º — arcsin(3/4) — with respect to the normal (perpendicular to the surface) so it acts as a wide-angle lens with a 97º angle into the camera. Outside of that circle what you are seeing is light from inside the pool undergoing total internal reflection — the camera is immersed only about 10 cm or so, and the blue you are seeing is from the sides and bottom of the pool.