Lenses and Mirrors Help (page 2)

By — McGraw-Hill Professional
Updated on Sep 18, 2011

The Convex Mirror

A convex mirror reflects light rays in such a way that the effect is similar to that of a concave lens. Incident rays, when parallel, are spread out (Fig. 17-6 A ) after they are reflected from the surface. Converging incident rays, if the angle of convergence is just right, are collimated by a convex mirror (see Fig. 17-6 B ). When you look at the reflection of a scene in a convex mirror, the objects all appear reduced. The field of vision is enlarged, a fact that is used to advantage in some automotive rear-view mirrors.

Optics and Telescopes Basic Optics The Convex Mirror

Figure 17-6. At A a convex mirror spreads parallel incident light rays. At B the same mirror collimates converging incident light rays.

The extent to which a convex lens spreads light rays depends on the radius of curvature. The smaller the radius of curvature, the greater is the extent to which parallel incident rays diverge after reflection.

The Concave Mirror

A concave mirror reflects light rays in a manner similar to the way a convex lens refracts them. When incident rays are parallel to each other and to the axis of the mirror, they are reflected so that they converge at a focal point (Fig. 17-7 A ). When a point source of light is placed at the focal point, the concave mirror reflects the rays so that they emerge parallel (see Fig. 17-7 B ).

The properties of a concave mirror depend on the size of the reflecting surface, as well as on the radius of curvature. The larger the light-gathering area, the greater is the light-gathering power. The smaller the radius of curvature, the shorter is the focal length. If you look at your reflection in a convex mirror, you will see the same effect that you would observe if you placed a convex lens up against a flat mirror.

Optics and Telescopes Basic Optics The Concave Mirror

Figure 17-7. At A a concave mirror focuses parallel light rays to a point. At B the same mirror collimates light from a point source at the focus.

Concave mirrors can have spherical surfaces, but the finest mirrors have surfaces that follow the contour of an idealized three-dimensional figure called a paraboloid . A paraboloid results from the rotation of a parabola, such as that having the equation y = x 2 in rectangular coordinates, around its axis. When the radius of curvature is large compared with the size of the reflecting surface, the difference between a spherical mirror and a paraboloidal mirror (more commonly called a parabolic mirror ) is not noticeable to the casual observer. However, it makes a big difference when the mirror is used in a telescope.

Practice problems of this concept can be found at: Optics and Telescopes Practice Problems

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