Here B is a surface of any form, illuminated by rays from A. At the distance C, twice as far, it is plain that the same light, diverging on every side, will cover 4 times as much surface, and at D, 3 times as far, it will be spread over 9 times as much space, and so on: but since the whole quantity of light is the same throughout, if it is spread over 4 or 9 times the surface, it must be 4 or 9 times weaker, that is, in proportion as the square of the distance. Hence images grow rapidly faint as they are formed further from the mirror, and the reverse.

The virtual images at the back of the mirror are not inverted, because the rays have not crossed at C: they are also larger than the object, being formed further from the mirror.

Large concave mirrors may be employed in light-houses, or in night-signaling. For a brilliant light being placed in PF, the reflected rays will go out nearly parallel to any assignable distance, and may be directed upon any special point by moving the mirror.

As the reverse of this application, large concave mirrors may be employed to concentrate the sun's rays at PF, and produce surprising results in burning, fusing, and volatilising almost everything on which the solar image falls. Much has not been attempted in this direction, though

the modern substitution of silvered glass for metal would render such experiments more feasible. A mirror of 6 feet (72 inches) in diameter and 10 feet in focal length would form an image of the Sun 1 inch in diameter1, in which the heat would exceed the ordinary solar heat in the proportion of 12 to 722, more than 5000 times, and as in putting the solar heat as low as 100° Fahrenheit, we should much more than allow for loss of light in reflection, we could reckon upon the almost inconceivable temperature of at least 500,000°. Few sub

stances could be found to withstand such heat; almost every known material would be melted and dissipated. Such a mode of concentrating heat has of late been employed with great success by M. Mouchot, in the clear Algerine sky, for distillery purposes, and as a substitute for steam-power.

Many curious illusions may be produced by large concave mirrors; the object and mirror being concealed, and the image received on smoke, or on some suitable screen, or the eye being placed in the reflected rays.

1 As the sun's rays are practically parallel it might be at first supposed that the focal image would be a point: and so it would be if the sun were a point. But he is a broad disc, composed of innumerable points, each one of which forms its image in the focus, so as to produce a corresponding disc there.

The Convex Mirror is the reverse of the concave in every respect. The Ps instead of converging will diverge from the centre, which will be behind the mirror, and the reflected rays will diverge from virtual foci behind it, instead of converging to real ones in front of it. It has therefore no power of forming a real image, since the rays never cross, and the virtual images behind or within its surface are erect, and always smaller than their objects outside. Hence it

can represent in a small compass the whole interior of a room; and was formerly much used as a piece of ornamental furniture.

To these three cases of Plane, Concave, and Convex Mirrors we may add some other forms of polished surfaces, such as cylinders and cones, which are seldom met with; and more familiar combinations of curves, the distorting effects of which we recognise when we see our faces reflected by a spoon. But the same law is preserved, even in its most perverted applications.

Reflection however is not confined to polished

D

surfaces; which are not the most common. Every object around us, except such as may be self-luminous, or black from reflecting no light, is seen no otherwise than by the light which it reflects, and which from the roughness of its surface is diffused in every direction, and meets the eye in every position. This is called Irregular, or Diffused Reflection. Not only solid and liquid bodies, but even some gases, are visible in this way; and the brightness and blueness of the sky by day, and the morning and evening twilight, are due to the reflective power of the air. But for this, the noon-day sky would be black, as it must be on the Moon, which has so little atmosphere; and every object not in sunshine, or not aided by reflection from neighbouring objects, would be in absolute darkness. Such is the case in a telescopic view of the moon, where the shadow of every mountain is as midnight; while the shadows on earth, viewed from a distance, would be softened and lightened by that atmospheric reflection, which contributes a very material though little suspected amount of convenience and comfort to the existence of man.

We now proceed to another of the principal properties of light We must Refraction.

leave Reflection for the present as completely

behind as if we had never learned it, and apply ourselves to a new rule and fresh phænomena.

Light may not only be turned back, as we have seen, from a polished surface without entering, as in Reflection, but may enter in, and be bent up or down, right or left, or in fact in any direction, in the very act of entrance; and this bending is called Refraction. Some of it is always reflected1; but a portion passes in, and we are to learn which way it will go. Now if a ray passes from one transparent medium to another, it is always refracted or bent, if the media are of different density. By density we mean the amount of matter in a certain space; so that one medium is more or less dense than another according to the quantity of matter it contains. So glass is denser than water, water denser than air. Many other transparent media might be named, alcohol, spirit of turpentine, oil, ice, crystals, the diamond. But we shall keep to glass, water, and air; they will answer every purpose, with less risk of confusion.

This then we are distinctly to understand, that whenever the density of a medium changes, the path of light within it changes; it is refracted, or bent, into a fresh line, as straight 1 See however note on p. 16.