1. The law of reflection: plane surface.

When light reflects from a plane surface as shown in Figure 3-5, the angle that the reflected ray makes with the normal (line perpendicular to the surface) at the point of incidence is always equal to the angle the incident ray makes with the same normal. Note carefully that the incident ray, reflected ray, and normal always lie in the same plane.

The geometry of Figure 3-5 reminds us that reflection of light rays from a plane, smooth surface is like the geometry of pool shots “banked” along the wall of a billiard table.

With the law of reflection in mind, we can see that, for the specular reflection shown earlier in Figure 3-4a, each of the incident, parallel rays reflects off the surface at the same angle, thereby remaining parallel in reflection as a group. In Figure 3-4b, where the surface is made up of many small, randomly oriented plane surfaces, each ray reflects in a direction different from its neighbor, even though each ray does obey the law of reflection at its own small surface segment.

2. Reflection from a curved surface.With spherical mirrors, reflection of light occurs at a curved surface. The law of reflection holds, since at each point on the curved surface one can draw a surface tangent and erect a normal to a point P on the surface where the light is incident, as shown in Figure 3-6. One then applies the law of reflection at point P just as was illustrated in Figure 3-5, with the incident and reflected rays making the same angles (A and B) with the normal to the surface at P. Note that successive surface tangents along the curved surface in Figure 3-6 are ordered (not random) sections of “plane mirrors” and serve—when smoothly connected—as a spherical surface mirror, capable of forming distinct images.

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