A Text-Book of Astronomy

by George C. Comstock

The condensation of wave energy in the circular and elliptical buckets are special cases under the general principle that such a condensation will be produced at any point which is so placed that different parts of the wave front reach it simultaneously, whether by reflection or by some other means, as shown below.

The student will note that for the sake of greater precision we here say wave front instead of wave. If in any wave we imagine a line drawn along the crest, so as to touch every drop which at that moment is exactly at the crest, we shall have what is called a wave front, and similarly a line drawn through the trough between two waves, or through any set of drops similarly placed on a wave, constitutes a wave front.

77. Mirrors and lenses.—That form of radiant energy which we recognize as light and heat may be reflected and condensed precisely as are the waves of water in the exercise considered above, but owing to the extreme shortness of the wave length in this case the reflecting surface should be very smooth and highly polished. A piece of glass hollowed out in the center by grinding, and with a light film of silver chemically deposited upon the hollow surface and carefully polished, is often used by astronomers for this purpose, and is called a concave mirror.

The radiant energy coming from a star or other distant object and falling upon the silvered face of such a mirror is reflected and condensed at a point a little in front of the mirror, and there forms an image of the star, which may be seen with the unaided eye, if it is held in the right place, or may be examined through a magnifying glass. Similarly, an image of the sun, a planet, or a distant terrestrial object is formed by the mirror, which condenses at its appropriate place the radiant energy proceeding from each and every point in the surface of the object, and this, in common phrase, produces an image of the object.

Another device more frequently used by astronomers for the production of images (condensation of energy) is a lens which in its simplest form is a round piece of glass, thick in the center and thin at the edge, with a cross section, such as is shown at A B in [Fig. 38]. If we suppose E G D to represent a small part of a wave front coming from a very distant source of radiant energy, such as a star, this wave front will be practically a plane surface represented by the straight line E D, but in passing through the lens this surface will become warped, since light travels slower in glass than in air, and the central part of the beam, G, in its onward motion will be retarded by the thick center of the lens, more than E or D will be retarded by the comparatively thin outer edges of A B. On the right of the lens the wave front therefore will be transformed into a curved surface whose exact character depends upon the shape of the lens and the kind of glass of which it is made. By properly choosing these the new wave front may be made a part of a sphere having its center at the point F and the whole energy of the wave front, E G D, will then be condensed at F, because this point is equally distant from all parts of the warped wave front, and therefore is in a position to receive them simultaneously. The distance of F from A B is called the focal length of the lens, and F itself is called the focus. The significance of this last word (Latin, focus = fireplace) will become painfully apparent to the student if he will hold a common reading glass between his hand and the sun in such a way that the focus falls upon his hand.

Fig. 38.—Illustrating the theory of lenses.

All the energy transmitted by the lens in the direction G F is concentrated upon a very small area at F, and an image of the object—e. g., a star, from which the light came—is formed here. Other stars situated near the one in question will also send beams of light along slightly different directions to the lens, and these will be concentrated, each in its appropriate place, in the focal plane, F H, passed through the focus, F, perpendicular to the line, F G, and we shall find in this plane a picture of all the stars or other objects within the range of the lens.