Why does this happen?

The waves on the water act as millions of concave and convex mirrors. So it is actually reflection of lunar light rather than refraction of light we are seeing. The waves provide a huge, but not quite infinite, number of potential reflective surfaces to work with. Typically, the larger and rougher the waves are, the wider the reflected image appears.

As you may have experienced in a fun house maze, concave and convex mirrors can appear to shrink or enlarge the image it reflects. This is why the reflected image of the moon on waves is much larger than the image of the moon in the sky. All the reflected images experience constructive interference, that is they are added together.

The image is brightest near the center as there are more available combinations of mirror curvature at those angles which will allow light from a diffuse source such as the moon (it subtends about a half degree of arc in the sky) to reach our eye.

As the angles between the observer and the moon increase, there are fewer reflective surfaces in the waves which will provide a successful reflection option. This causes the image to fade out near the edges.

If the water becomes very calm, it can lay as flat as a bathroom mirror. In this condition of no waves, the lunar image becomes a single disk of light, just as viewed in the sky.

The image moves along with you as you walk in exactly the same way your image in a mirror moves with you as you walk. The combination of reflective surfaces and angle combinations create the image in relation to the source, reflective surface and the observer.

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The light strip you see starts getting dimmer at it s edges , and is brightest at its center. It s actually the rays of light from the moon , which are able to reach your eyes after refraction by the water. The whole water body isn t illuminated , because the light rays falling on the un-illuminated parts , are refracted in other directions , not reaching your eyes.