From smooth to rough

A smooth reflection

Standing at the edge of a large lake, you can see the mountain peaks directly and also in a perfect reflection of the mountain from the water.

Remember that you can draw rays to predict. Draw two rays from a pair of selected points—one near the top of the mountain, and one near the bottom.

To model the direct view of the mountain draw rays travelling straight from those points to your eye. To model the reflection of the mountain, draw rays travelling down to the lake surface from the mountain, then reflected from the flat surface to your eye.

To get further you'll have to learn more about the eye.

Drawing rays inside the eye

Redraw the eye more and more simply (ending with a pinhole eye). Draw rays for the original view of the mountains.

The direct and reflected rays swap, top for bottom, and bottom for top. Therefore the eye will see the mountain up the right way up and upside down. Most brains choose to show the reflection upside down.

Find a mountain and a lake on a clear still day and see if the predictions are correct.

A rippled surface

Just then, a sudden squall of wind blows up across the lake, disturbing the water's surface. The reflected image of the mountain disappears as the rays of light are now reflected in all directions. Use the models you've just drawn to make sense of this.

For each ray, the angle of incidence is equal to the angle of reflection. The rays strike different regions of water, which are at different angles. The rays are reflected at many different angles and the image is jumbled up. The more ripples and the steeper the ripples, the worse the jumbling up. Just like diffuse reflection from the stones in the wall.