If two thin lenses of focal lengths f, and f, are put close together with their axes coinciding, they form a lens whose focal length. f. is given by the formula 1 1 1 f f if the two lenses arc at a distance d apart, the focal length of the combination f is given by the formula 1 1 , 1 If the lens is not thin, but so thick that this fact must be taken into it may be proved that tlmre are two planes perpendicular to the axis, either in the lens or near it, which are so placed that if u is the distance from the source to one plane and r that from the image 0' to the other, the same formula as be fore applies. These planes are called the 'prin cipal planes.' They have other important proper ties also; hut for a lull discussion of thick lenses and their combination reference must be made to some treatise on optics.
Lenses and systems of lenses as used in micro scope,. telescope-. photographic len-e-. •tc., are subject to the following—among other—imper fections: / oblique ray from a point on the axis does not pass through the same fawns as does a homoeentrie pencil.
(2) Curraturc of Field.—The image of a plane figure perpendicular to the axis will not be formed a plane. but on a curved surface.
Distort ion.—The image of a large object. e.g. a building, is not similar in all its parts to the parts of the object; the magnification may be different and a rectangular portion of the object may appear in the image with curved edges.
(41 If the image of a small plane area perpen dicular to the axis is formed by a lens which is large compared with the object. the image is not a small plane area perpendicular to the axis unless Ahhe's 'sine formula' is satisfied. if the system satisfies this condition. it is called apla natie.
(3) Chromatic Aberration.—Owing to tlie fact that the index of refraction differs with the color of the light, there are different focal lengths for rays of different color; and. further, if the lenses are thick, the magnification is different also. See ACHROMATISM.
Many of these imperfections can be avoided by a suitable choice of material for the lenses. by proper curvature for the lens-surface, and by using suitable combinations of lenses. Lens comhination, which are free from certain errors are called special names. A photographic lens free from distortion of field is called 'ortho seopic;' one free from curvature of field and from chromatic and spherical aberrations is called 'anastigmatic:' a microscopic objective free from secondary spectra of aberrati4,a and aplanatic for several colors. 'apochromatie,' Several facts should be borne in n ind in re gard to an optical combination: f 11 The intrinsic brightness of any surface cannot be increas. d by
any optical means. The natural brightness of any object—that is. the light received per -quire centimeter of the image on the retina of the eye when looking directly at the great as the brightness when looking at the object a telescope or mieroscope. The hright ness of a star or point-source may. however. be increased by using a tele•eope, because by means of it more light is brought into the eye: the increase is in general proportional to the ratio of the area of the object-glass of the telescope to that of the iris of the eye. 3) No amount of magnification will enable one to 'resolve' two point-sources—that is, to see them as two sep arate objects—if they are as close together as a certain fraction of the wave-length of the light which they are emitting. This fact depends upon the properties of diffraction of the ether-waves, and will be discussed later. For detailed de scription of various optical 1 ni Men t,, see the art ieles NlIttioscom:; TELESCOPE; SPECTRO :•tom., etc.
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In this branch of light the assumption is made that the sensation called light is due to the re ception into the eye of trains of waves. A 'source of light' is then a source of waves, which are propagated from the source to the eye—Or to Whatever instrument is used to detect their pres ence=and produce there certain effects. The phenomena to be considered are then: (1) the fact that trains of WaVP, carry energy: (2) the fact that waves are propagated with a finite velocity; (3) the kinematic properties of com position of wave-motion.
Pnorrommtv (q.v.) is that division of 'light' which is concerned directly with the comparison of quantities of light emitted by various sources and received by different bodies. If a point source emits in all directions a 'quantity of light' Al, its 'intensity' is said to be i.e. the quantity of light going out through a unit solid angle. This intensity is written I. A small sur face of area A, at a distance r from the point source. and inclined to the line joining it to the point-souee so that the angle between this line and a line perpendicular to the surface is 0, re 1 Acos0 ceives therefore an amount of intensity of 'illumination' of this surface is the amount of light per square centimeter; it is Icos0 written E. Bence E = r • Therefore the illumination varies directly as the intensity of the light, inversely as the square of the dis tance, and as the cosine of the obliquity of the surface.