Physics, Geometry
	Reflection of light, reflection off cushions, congruent triangles
	The well-executed bank shot in billiards can appear as a matter of luck. Using the physics of mirrors, a player can substantially increase success.

A billiard ball hitting off a cushion will follow a symmetrical path. This is identical to the path that a beam of light will follow after hitting a mirror. The similarity allows one to better predict where a ball hitting a cushion will travel.

The diagram below shows the path of a cue ball hitting a cushion or the equivalent path of a light beam hitting a plane mirror.

The dotted line in the diagram is called the normal line. It is a line drawn perpendicular to the reflecting surface.

The light ray and the normal to the surface define the angles of the light. They are named the angle of incidence and the angle of reflection. The angles are equal, as can be seen in the diagram.

It is this equivalence of the angles that makes images in a mirror appear identical to the object. To see an object in a mirror, light must scatter off the object, reflect off the mirror and enter our eye. Looking at two rays of light, we can trace the paths taken.

The rays of light enter the eye as shown in the diagram on the right. The eye “assumes” that light travels in straight lines. It therefore sees an image of the object on the other side of the mirror. This image is identical in appearance and is located the same distance behind the mirror as the object is in front of the mirror.

Since a billiard ball follows the same path that the light does, we can imagine that the cushion of the pool table is a mirror. We can then aim at the reflection of the pocket in the reflection of the table.

The billiard ball will reflect off of the cushion and head for the pocket.

This technique can be extended to include a bank shot off of two cushions. Here we have to imagine both cushions as mirrors. There are now three images of the pockets. The first is the image off the first cushion, the second is the image off the second cushion, and the third is the image of the first cushion off the second cushion. The image of the second cushion off the first cushion is identical to the third image, as you can see in the diagram.

Imagine these reflections and aim for the third image, and the ball traces the path shown in the pool table. Notice that the angle of incidence always equals the angle of reflection.

Experiment with the images of mirrors. Place a small flat mirror vertically on a piece of cardboard. You can hold it in place with a piece of clay. Stick a pin into the cardboard and note the reflection. Add a second mirror perpendicular to the first. Count the images seen. Continue the experiment by changing the angle between the mirrors. When the angle between the mirrors is 60°, there should be five images. Are you able to see them all? Graph the relationship between the angle between the mirrors and the number of images. Derive a mathematical equation to predict the number of images given the angle between the mirrors.