The enigmatic bright line at the horizon

Have you noticed the bright line at the horizon, where the surface of a lake meets the dark outline of land? It fascinates me, makes me wish to go there. But that is probably as impossible as it is to reach the rainbow. Of course, it might be a shore of white sand, over there, but more likely it's an optical phenomenon. Probably only seen under certain conditions -- but what are they? I haven't bothered to find out under what circumstances I have observed the phenomenon.

Painters also love it, I am sure. As in the following study of a peaceful summer evening, by the Swedish artist Severin Nilsson.



M. Minnaert (in his lovely little book "Light and Color in the Open Air") doesn't mention this bright line explicitly, but it must be closely related to what he has to say about how the sun, or moon, or a distant cloud, is reflected in the sea, if the sea is neither very calm nor very stormy. As a rule, the image is shifted towards the horizon. The explanation is as follows: at a great distance we can only see the sides of the waves turned towards us. This makes it seem as if we saw all the objects in the sky reflected in a slanting mirror. It is thus important that the surface of water is very wide. The calmer the surface, the more obliquely one has to look.

This explains the evident fact that one does not see any dark mirror image of the coast, below it, as one should if the water surface was perfectly even (and thus horizontal). Instead this bright line, where darkness would be expected ...

I assume that the increased brightness of the reflection, as compared to the brightness of the water surface nearer the observer, is a kind of perspective effect; that is, the farther away we look, the wider extent of water corresponds to a given visual angle. Thus more reflected light from the sky goes into that angle, so to speak. The narrow line, over there, in reality corresponds to quite a vast extent of water. Like a rainbow, it would recede if one moves closer, eventually disappearing totally.

Do you agree with this tentative explanation, my dear reader? Anyway I am not sure it will suffice to explain the fact that we see such a distinct line, rather than a softer luminance gradient. To find out, one has to make a quantitative modelling and calculation.

© Pehr Sällström 2006