What is Snell's window?

Why is it that an underwater observer can see only a circular "window" and also can't see anything above the separating surface? Does the "window" depend on the depth?

• This video shows what it looks like in a swimming pool: youtube.com/watch?v=FG6ryu0-C5w. Notice that the "window" resembles a fisheye lens: everything above water is visible, the field of view is 180° – jkien Mar 6 at 23:10

Beyond a certain angle total internal reflection occurs at the water-air interface. This is because Snell's law $$\sin \theta_{air} = n \sin \theta_{water}$$ has no solution for $$\theta_{air}$$ if $$n \sin \theta_{water} >1$$ or $$\theta_{water} >\sin^{-1}(1/n)$$.