A spherical mirror is a mirror which has the shape of a piece cut out of a spherical surface. There are two types of spherical mirrors: concave, and convex. These are illustrated in Fig. 68. The most commonly occurring examples of concave mirrors are shaving mirrors and makeup mirrors. As is well-known, these types of mirrors magnify objects placed close to them. The most commonly occurring examples of convex mirrors are the passenger-side wing mirrors of cars. These type of mirrors have wider fields of view than equivalent flat mirrors, but objects which appear in them generally look smaller (and, therefore, farther away) than they actually are. |
Figure 68: A concave (left) and a convex (right) mirror|
A convex mirror is a spherical reflecting surface (or any reflecting surface fashioned into a portion of a sphere) in which its bulging side faces the source of light. Automobile enthusiasts often call it a fish eye mirror while other physics texts refer to it as a diverging mirror. The term “diverging mirror” is based on this mirror’s behavior of making rays diverge upon reflection. So when you direct a beam of light on a convex mirror, the mirror will allow the initially parallel rays that make up the beam to diverge after striking the reflective surface. Since convex mirrors have wider fields of view than other reflective surfaces, such as plane mirrors or concave mirrors, they are commonly used in automobile side mirrors. Having a fish eye on your automobile will allow you to see more of your rear. The complete description of an image formed by a convex mirror is: virtual, diminished in size, and upright. When we say upright, we mean that if you position an arrow in front of this kind of reflecting surface, then the arrowhead of the reflection will point to the same direction as that of the object (the real arrow) itself.
Sometimes referred to as a converging mirror, the concave mirror is made with a surface that bends inward. Because the center of the curve is directed away from any incident light, it creates a reflection that is typically larger than the actual focal point. This type of mirror is considered a converging device because it collects the light that falls into the bowl created by the inward bulge of the surface. This collection causes the light to refocus into a single focal length. The light is collected at different angles, since the concave nature of the bulge allows the light rays to make normal contact at differing depths at each point on the surface of the mirror. The unique reflection that is created by a concave mirror makes the device extremely useful in a number of different devices. One of the most common applications is with the production of automobile headlights. By placing the source of light at the center of the mirror reflector, the result is a parallel beam of light that provides both good visibility for the driver of the car as well as points of light that are obvious to approaching vehicles. As illustrated in Fig. 69, the normal to the centre of the mirror is called the principal axis. The mirror is assumed to be rotationally symmetric about this axis. Hence, we can represent a three-dimensional mirror in a two-dimensional diagram, without loss of generality. The point at which the principal axis touches the surface of the mirror is called the vertex. The point , on the principal axis, which is equidistant from all points on the reflecting surface of the mirror is called the centre of curvature. The distance along the principal axis from point to point is called theradius of curvature of the mirror, and is denoted . It is found experimentally that rays striking a concave mirror parallel to its principal axis, and not too far away from this axis, are reflected by the mirror such that they all pass through the same point on the principal...