If you happen to lie at the bottom of a swimming pool and look up at the sky, you will see the 180° view of the area above the water compressed into an angle of about 97°, confining your field of view to a circular window of water, known as Snell’s window: a consequence of refraction. The area outside the window appears dark.

Of course, this has been known for a long time and the phenomenon has been seen and photographed frequently; you can do a quick search of the term and will see a lot of photographs of this effect taken by amateur and professional photographers and divers.

The author of this paper gives an interesting study of the optical effects of waves on Snell’s window. In calm conditions, when the water surface is flat, the angular span of Snell’s window is 97°. According to the author’s calculations, in the presence of waves on the surface of water, this window can range from 97° to 122° and in the case of breaking waves this window can cover the entire 180° field of view equaling the upper hemispherical area outside the water.

It is quite interesting to realize that water waves can have such a huge effect on the refraction of light that under certain conditions, such as breaking waves, the overall effect of refraction becomes negligible underwater. Also, the dark region around the Snell’s window is not so dark in shallow waters due to scattering of sky light within the water and some back-scattering contribution from the bottom. Turbidity can also add to the brightness of the dark region but all of the brightness in this region is contributed from back scattering and reflection of light from the bottom surface.

This study explains the role played by the dynamics of waves and breaking waves affecting the refractive properties of light in water and might be helpful in certain underwater activities.

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