8.3 Ray Diagrams

Now that a few basic principles of light behavior are known, it is possible to start making predictions about their paths. We can do this using diagrams known as ray diagrams, which make use of the model of light as traveling in a straight line.

Reflection is a principle that we experience every day - as often as looking in the mirror. What happens to the image of a pencil when it is reflected in a mirror ? Where is the image located ? Let’s find out.

Here is a pencil in front of a mirror. To make it easier to draw a ray diagram, we will call one end of it A, and the other B, while from this point on, the mirror will be represented as a line.

We will start by constructing the image of point A. First, pick two points. Next, draw a line through each of the points and point A, continuing them until they reach the mirror. These lines represent the two of the infinite number of rays that emanate from point A on the pencil. Keep in mind that any two such rays that are directed at the mirror could be used to draw a ray diagram. Once these rays reach the mirror, they are treated as incident rays. On the following diagram, these are shown in blue. By constructing two normals, the reflected rays can be constructed. These are shown in green.

Finally, the reflected rays are extended "behind" the mirror, towards their apparent origin, until they intersect at that origin. This new point is the reflected image of A.

The image of B can be constructed in the same way, and the final image of the pencil is shown here:

You can see that the orange side of the pencil remains the farthest from the mirror in both reflection and image, meaning that the image has been effectively "flipped" over the line of the mirror. The new image is also the same size as the original, and the same distance away from the mirror as the pencil.

Next, let’s look at what happens when a light ray is shone into the following glass shape below, at the point marked.

It is refracted by the glass, but, because any radius of a semicircle (the shape of the glass) is perpendicular to the surface, it is not refracted again upon exiting. Any ray shone into this part of the semicircle is refracted only once:

Look at the orange and purple rays in the diagram above. When they enter the semicircle, they are quite far apart (in terms of the angle between them). However, when they leave the semicircle, they are much closer together. This is one of the ideas behind a converging lens.

Now that you have seen what happens when you shine a ray onto one part of the semicircle, you are probably wondering what happens when the ray is on a different part. The result is quite different. This time, rays do not follow the radius of the semicircle, and therefore are refracted not only upon entering the glass, but upon leaving it as well.

However, an interesting effect results from shining rays that are perpendicular to the flat surface of the semicircle into it.

All these rays, which are necessarily parallel to each other, converge once they have gone through the semicircle. These rays are also only refracted once. When they enter the semicircle, because the are already at the normal to the surface, they are not refracted, but when each leaves the circle, it is refracted a different amount, due to the different curvature at the points they exit. This idea of convergence at a point is another important principle of converging lenses, which will be discussed next.