Why is the measurement made to the normal line?

Choosing the normal line

You might wonder why the angles of incidence and reflection are measured between the rays and the normal line, and if you don't there is a good chance that one of your pupils will ask about this. For a flat or plane mirror we could take either the angle between the ray and the normal line, or the angle between the ray and the mirror. In each case the designated angles of incidence and reflection will be equal.

However, if we are using mirror which is a curved surface things are not so straightforward. To measure any angle we need two straight lines, for a curved mirror we might be tempted to pick the tangent as our second line. However, for a curved surface there are many different tangential lines (in fact making a tangential plane) but just one, unique normal line. This makes the normal line the easiest option for more complicated mirror shapes, so the convention is to measure all angles of incidence and reflection in relation to the normal line.