(4) When two mirrors are placed paral lel to one another, light from an object between them is reflected back and fore, so as to appear on each occasion of re flection as if it came from images more and more remote from the mirrors. On each occasion the course of the rays of light is the same as if the virtual image behind the mirror had been a real object; and a new virtual image is pro duced, apparently as far behind the re flecting mirror as the virtual object had been in front of it. If the mirrors were perfectly plane and parallel, and if they reflected all the light which fell on them, an observer between the mirrors would see in this experiment (which is called the endless gallery) an indefinite num ber of images. A variation of this experi ment, carried out with mirrors not par allel to one another, but inclined at an angle which is some aliquot part of 180°, gives the principle of the kaleidoscope.
(5) When a beam of light is reflected from a mirror and the mirror is turned through a given angle, the reflected beam is swept through an angle twice as great. This principle is utilized in the con struction of many scientific instruments, in which the reflected beam of light serves as a weightless pointer, and en ables us to measure the deflection of the object which carries the mirror. (6) When a beam of light is reflected at each of two mirrors, inclined at a given angle, the ultimate deviation of the beam is (if the whole path of the light be within one plane) equal to twice the angle between the mirrors. This proposition is applied in the quadrant and sextant. (7) When a wave of any form is reflected at a plane surface it retains after reflection the form which it would have assumed but for the reflection, this form being, however, guided by reflection into a dif ferent direction.
Curved Reflecting Surf aces.—In these we have to trace out the mode of reflec tion of incident rays from each "ele ment" or little bit of the reflecting sur face; and this leads, through geometrical working, to such propositions as the fol lowing: (1) Parallel rays, traveling parallel to the axis of a concave parab oloid mirror are made to converge so as all actually to pass accurately through the geometrical focus of the paraboloid; and, conversely, if the source of light be at the geometrical focus, the rays re flected from the mirror emerge parallel to one another—a proposition of great utility in lighthouse work, search-lights, etc. (2) If the paraboloid mirror be convex, parallel incident rays have, after reflection, the same course as if they had come from the geometrical focus of the paraboloid. (3) In a concave ellipsoid
mirror, light diverging from one "focus" of the ellipsoid is reflected so as to con verge on the other "focus" of the curved surface; and by a convex ellipsoidal mir ror light converging toward the one focus is made to diverge as if it had come directly from the other focus. (4) In a hyperboloid reflector the two geometrical foci have properties corresponding to those of the ellipsoid. (5) In spherical reflectors, which are those most easily made, there is no accurate focus except for rays proceeding from the center and returning to it. When parallel rays are incident on a concave spherical mirror we see that if they be parallel to the axis of the mirror each ray is made to pass after reflection through a point, which is nearer to a point midway be tween the mirror and its center, the narrower is the pencil of rays. If there fore, the pencil of rays be very narrow in comparison with the radius, the rays will, after reflection, approximately con verge on the midway point, which is called the principal focus of the mirror. The reflected rays from the various parts of the mirror form by their intersection a caustic, the apex or cusp of which is at the midway point.
As to the quality of the light reflected there are some peculiarities to be ob served. From the surface of a trans parent body, of greater optical density than the surrounding medium, light polarized in the plane of incidence and reflection is more largely reflected at oblique incidences than light polarized at right angles to that plane; when the angle of incidence is such that the re flected and refracted rays tend to be at right angles to one another, the whole of the light reflected is polarized in the plane incidence and reflection; and if light polarized at right angles to that plane be made to fall on glass at the particular angle of incidence just re ferred to, it will not be reflected at all, but will wholly enter the glass. Plane polarized light polarized in any other plane than that of incidence or one at right angles to it, is, after total reflec tion in glass, found to be elliptically po larized; and this phenomenon is always presented in reflection from metals. In the case of electromagnetic radiation theory and practice concur in indicating that conductors are good while non-con ductors are bad reflectors; and the same general proposition holds good with ref erence to those more frequent but other wise similar ether oscillations to which the phenomena of radiant heat, light, and actinism are due.