rors, because all the rays of light which fall on them are reflected in a diverging direction.

Determination of the Principal Focus. It is often necessary to find the radius of curvature, which of course is double the focal distance. To obtain this distance from a concave mirror, cause the rays of the sun to be reflected from the mirror to a ground glass screen; move the screen until they converge and give a bright luminous spot; then the distance from the mirror to the screen is the true focal distance.

In a convex mirror, to determine the principal focus is a more difficult matter, because it is virtual. Cover the mirror with paper, leaving two small holes ; allow the reflected light from these to fall upon a ground glass screen; move the screen backwards until the distance between the two luminous spots on the screen is exactly double that between the openings on the mirror. The mathematician will at once see that the distance between the mirror and the screen, reckoning from the mid point between the luminous spots in each case, represents the focal distance of the mirror.

So far we have considered points chiefly; to understand the formation of figures by these mirrors it is only necessary to imagine the figure to be made up of a series of points, and to judge of their position according to the principles already laid down. The student is advised to practise this part of the subject by drawing various figures in different positions as constantly seen by the eye.

Ordinary mirrors

Application of Mirrors. are too well known to require alluding to. Concave mirrors have been employed as burning mirrors, —that is, for concentrating the heat of the sun's rays on an inflammable substance. They are used in

telescopes, and an instrument called the heliostat is formed by mirrors arranged so as to move in any direction, and throw the sun's light in any required course. For lighthouses such mirrors have been used, though they have been supplanted by parabolic mirrors, which prevent the diffusion and consequent weakening of the intensity of the light. A little thought will readily suggest to the student that a parabolic mirror will reflect the rays of light in straight lines, which is not the case with a concave mirror. The difference is not great, but appreciable in long distances.

Aberration of Sphericity by Reflection. Caustics. When the angle of aperture exceeds 10° it will readily be seen that the successive reflections will cross each other instead of coming to a focus at a certain point; and the places where they cross being united by a line drawn through them will give a curve, which is called a caustic by reflection, to distinguish it from a caustic by refraction, which will occur in the description of lenses. The caustic is said to be caused by aberration of sphericity.

321

m

3

Fig. 40.

The ray G 4 will be focussed at F.

G 3 a little nearer the mirror, so as to cross line 4 F. G 2 still a little nearer, and so on. This is called aberration

of sphericity by reflection; the line joining the crossing points, as F m, is termed a caustic.

Refraction of Light.-The bending or deviation which the rays of light undergo in passing from one medium to another is called refraction. A medium, in optics, is any substance through which light can pass. In optics, a medium is either dense or rare, according to its power of refracting light, and not according to its specific gravity. For instance, alcohol, olive oil, and turpentine have a less specific gravity than water, but have a greater refractive power. The laws which govern the refraction of light are as follow:

1. The planes of incidence and refraction coincide, both being normal to the surface separating the media at the point of incidence.

2. The sine of the angle of incidence is equal to the sine of the angle of refraction multiplied by a constant quantity.

The constant quantity referred to varies with the media, but is the same for any given medium. It is called the index of refraction.

B

Let A be the point of incidence in a line separating air from water. With A as a centre, describe the circle Bm C p. Let L A be an incident ray, and A k the refracted ray. Draw m n and bq perpendicular to the normal B C. Then will these lines bear the same proportion to each other that the sine of the angle of incidence bears to the sine of the angle of refraction, and we shall have, in the particular case of air and water, m n equal to p q multiplied by 13, whatever may be the inclination of L k,

k

Fig. 41.

Here is the index of refraction. For air and glass the index of refraction is 1. Suppose the ray of light to be passing from water to air, then the sine would be reduced in the same proportion as it is here increased, and the same consideration must be borne in mind with regard to glass or any other substance.

A straight stick partly immersed in water appears broken or bent at the point of immersion. This is owing to the fact that the rays of light proceeding from that part of the stick under water are refracted, or deviate from a straight line as they pass from the water into the air. That part of the stick in the water will appear lifted up or bent in such a way as to form an angle with the part out of the water.

The annexed diagram will assist the student to understand this. A B represents the true position of the stick; An C its apparent position. The dotted lines proceeding from the part immersed represent the rays which on emerging from the water are refracted, so as to enter the eye at m. The eye sees in the direction of the rays, and therefore these rays, continued in

m

Fig. 42.*

* The engraver has given the lines from B n to the surface perfectly vertical, if so they would not be refracted at all. Imagine them to be slightly oblique.

straight lines through the water, give the apparent position C of n B.

A spoon in a glass of water, or an oar partially immersed in water, always appears bent. A person endeavouring to strike a fish under water must, unless he be immediately above it, aim at a point apparently below it. Let a shilling be placed at the bottom of a basin, as at a (Fig. 43), in such a manner that the eye

Fig. 43.

at A cannot perceive it. Then let some one fill the basin gently with water, so as not to disturb the shilling. The coin now rises into view, just as if the bottom of the basin, had been elevated. It will, by the refraction, be seen not in its true place, a, but in the direction A B. The rays from the shilling, on entering the air, which has a much less refractive power than the water, are turned towards the surface of the water; and of the rays so emerging, some will proceed to the eye, and the image of the shilling will appear in the direction of the ray entering the eye. A clear stream, viewed obliquely from the bank, appears more shallow than it really is, since the light, appearing from the objects at the bottom, is refracted as it emerges from the water. The depth of water, under such circumstances, is about a third more than it appears-a useful fact for boys to bear in mind when bathing.