The points A and a, B and b and others similarly situated on an axis extending through the center of curvature C are called conjugate foci, for they are so related that an object being at either one, its image will be found at the other.
Fig. 362.—Action of a convex mirror upon parallel rays of light.
372. The Convex Mirror.—There are few practical uses to which convex mirrors can be put. They are sometimes used to give the chauffeur of an automobile a view of the road behind him. It is then attached to the wind shield by a short rod. The reflected rays coming from a Convex mirror are always divergent (see Fig. 362), hence the image is always virtual and located behind the reflecting surface. The method of construction for images formed by a convex mirror is similar to that for concave mirrors. (See Fig. 363.) The center of curvature and principal focus are behind the mirror and consequently the reflected rays have to be produced backward until they meet. The images are always virtual, erect and smaller than the object.
Fig. 363.—Construction of an image by a convex mirror.
Fig 364.—Illustrations of Spherical Aberration.
373. Spherical Aberration. Sometimes in a concave mirror when the aperture MCN (Fig. 364) is large the images are blurred or indistinct. This is due to the fact that the incident rays near the outer edge of the mirror do not focus after reflection at the same point as those which pass into the mirror near the vertex, but cross the principal axis at points between the mirror and principal focus as is shown in Fig. 364; this result is called spherical aberration. The larger the aperture of the mirror the more the image is blurred. Concave mirrors in practical use do not have an aperture much greater than 10 degrees. This non-focusing of the rays of light by curved reflecting surfaces may be noticed in many places, as when light is reflected from the inside of a cup that contains milk or from the inside of a wide gold ring placed on top of a piece of white paper. The pupil will note other instances. This curve of light observed is called the caustic by reflection.
374. Parabolic Mirrors.—The best possible surface to give to concave mirrors is parabolic. This is a curve which may be generated by moving a point so that its distance from a fixed point and a fixed line are always equal. If a source of light is placed at F the rays after reflection are rendered parallel. See Fig. 365. This reflector is used in automobile lamps, headlights of locomotives, search-lights, etc. It is also used in large reflecting astronomical telescopes to collect as large an amount of light as possible from distant stars and bring it to a focus. Such mirrors may be made exceedingly accurate.