REFLECTION 466 REFLECTION of all kinds, and therefore the theory of reflection has general reference to ra- diant heat, light, actinic radiation, and electro-magnetic undulations. Reflection arises in all cases from a difference in the transmissibility of ether disturb- ances on the two sides of the bounding surface. On reflection from polished surfaces we have, so far as regards the directions of the reflected rays, the following laws observed: (1) The incident "ray," the normal (i. e., a line draviTi perpendicu- lar) to the surface at the point of inci- dence, and the reflected "ray" all lie in one plane, the "plane of incidence"; and (2) the angle of incidence (the angle which the incident "ray" makes with the normal to the reflecting surface) is equal to the angle of reflection (the corre- sponding angle between the normal and the reflected "ray"). These laws apply equally to ether waves of all lengths, and therefore to light of all colors; and they also hold good whatever be the shape of the surface. If the surface be plane their application is simple; and if the surface be curved we have, in effect, to consider the curved surface as made up of indefinitely small facets, to each of which the above laws can be applied. The geometrical consequences of these laws make up what used to be called catoptrics, that part of geometrical optics which deals with reflection; and this coincides in its propositions with that part of kinematics, which gives an account of the reflection of waves. Here the other waves (using the term "waves" in its most general sense) are assumed to travel through optically ho- mogeneous media, and can consequently be traced out by imaginary lines drawn at right angles to the wave fronts or along the directions pursued by the waves, these imaginary lines being called "rays." Plane Reflecting Surfaces. — (1) Rays which are paralled to one another before striking a plane reflecting surface are parallel after reflection. (2) If light diverging from or converging toward a point be reflected from a plane mirror, it will appear after reflection to diverge from or converge toward another point situated on the opposite side of the mirror and at an equal distance from it. If, on the other hand, the course of the light is such that the rays appear before reflec- tion to converge on the second point, they will after reflection actually pass through the first one. (3) A consequence of the preceding proposition is that when an ob- ject Is placed before a plane mirror the virtual image is of the same form and magnitude as the object, and at an equal distance from the mirror on the other side of it. The right hand of the image taken as looking toward the mirror, is necessarily opposite to the left hand of the object; so that no one ever sees him- self in a single plane mirror as others see him or as a photograph shows him, but he sees all his features reversed. (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 lig;ht is reflected from a mirror and the mirror is turned through a given angle, the reflected beam is swept through an angle t^vice 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 vdthin 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 Surfaces. — 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
