Using Ray Diagrams to Solve Problems with the Law of Reflection

Like most "geometry" problems, geometric optics problems are most often solved with the aid of a drawing. The more careful the drawing, the more likely it is to assist you in solving the problem.

The figure below illustrates the law of reflection being used to show that you can see your entire body if you stand in front of a mirror which is half your height. In the figure,the relative postions of a woman and a mirror, one half her height, are shown. (The distance between them is not stated, and in fact, is not needed to solve the problem.)

A ray is drawn from the woman's foot to the mirror, where it is incident at the very bottom. The normal line is drawn at the point where the ray is incident on the mirror. Then the reflected ray is drawn so that the angle of incidence is equal to the angle of reflection. (Remember, both of these angles are measured from the normal, not from the surface.) The reflected ray does enter her eye, proving that she can see her foot if she looks toward the bottom of the mirror.

If you have a long mirror you can try this. In fact, if your mirror is covered so that its length is one half your height, you will be able to see your ankles when you look at the bottom of the mirror. As you walk away, you can still see your ankles! (Note that it doesn't really work well for your toes, since they are somewhat "ahead" of your eyes when you stand straight.)