Diffuse reflection of light

A smooth reflection

Imagine the scene. You are standing at the edge of a large lake, gazing out across the water at a range of mountains which rears up into the sky. You can see the mountain peaks directly and you are also aware that there is a perfect reflection of the mountain from the water. So you imagine two rays from a pair of selected points – one point near the top of the mountain, and one near the bottom.

To model the direct view of the mountain you imagine rays drawn straight from those points to your eye. To model the reflection of the mountain, you imagine rays drawn down to the lake surface from the mountain and being reflected from the flat surface to your eye.

How do these pairs show that the top and bottom will be reversed in the reflection?

The same rays, regrouped by the view to which they contribute

Here we've redrawn the scene, and hope that helps. Now the rays are grouped differently, with the rays coloured to show their origin.

To get further you'll have to model the eye as a pinhole camera (more on that in episode 02), to remember that the eye inverts all images that appear on the retina. You might like to draw out a ray diagram to see if you can figure out what is going on, before moving on.

Tracing rays inside the eye

Here we've simplified the eye (right down to a pinhole eye), taking the rays from the previous diagram. By the time it gets to be as simple as the pinhole camera, so just a box, you can very clearly see the predictions of the ray model of the original view of the mountains.

The green rays, predicting what the light beams from the top of the mountain will do, swap positions with the blue rays (that predict what the light beams from the bottom of the mountain will do) as you move from the reflected to the direct view, and back again.

As they swap position, top for bottom, and bottom for top, so the eye will see the mountain up the right way and upside down. Now all you need to do is 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. You can use the models you've just developed to make sense of this.

For each ray the angle of incidence is equal to the angle of reflection, but the incident rays strike different regions of water, which are inclined at different angles to each other. The outgoing rays are reflected at many different angles and so the image is jumbled up.