diminishes as the square of the distance from the luminous point. This may be illustrated by Fig. 1. Suppose the light of a candle to illuminate, at the distance of one foot, the surface of a screen one foot square, the same amount of light, at a distance of two feet, will spread itself over a screen four times as large, and at a distance of three feet, nine times as large. Since at these distances the same amount of light is diffused over areas respectively of four times and nine times the extent of the unit area, its intensity must diminish four times and nine times, or will vary inversely as the square of the distance.

M

R

N

FIG. 1.

FIG. 2.

When light falls upon a body, it may be disposed of in three ways. First, either reflected, that is, bent back; secondly, it may pass through the body in an altered direction, refracted; or thirdly, it may be absorbed.

In speaking of the properties of light, frequent use is made of the term ray, which must be understood to mean a single line of light. A pencil of light is a collection of rays diverging from or converging to a point. Mirrors are bodies of glass or metal with polished surfaces, which cause bodies presented to them to be seen by reflection.

REFLECTION FROM A PLANE SURFACE.-If a ray of light fall perpendicularly on a mirror, it is reflected back in the same line towards the point whence it came. When a ray of light, I O, falls obliquely on a plane mirror, M N, the incident ray is reflected in the direction O R, so that the angle P O R, formed with the perpendicular P O at the point of incidence, is equal to the angle, I O P, made by the incident ray with the same line. POR is the angle of reflection, I O P the angle of incidence. The two laws of reflection are the following: First, the incident and reflected rays are in the same plane; secondly, the angle of reflection is equal to the angle of incidence. A candle placed in front of the mirror, as at 1, would be seen by an eye placed at R as if at B, at a perpendicular distance behind the mirror equal to the perpendicular distance of the candle in front of it. The image is always seen in the direction the ray is travelling when it enters the eye. (Fig. 2.)

If a diverging pencil of light fall upon a plane mirror, the focus of the reflected pencil will be at the same distance behind the mirror as the focus of the incident pencil is in front of it.

Let I be the incident focus of a diverging pencil of rays, I O, I O', I O", any incident rays. Draw I P perpendicular to the mirror; taking the ray I O,

make P F equal to P I, and join F O. At o draw the perpendicular o X. From this construction it follows, from simple geometrical reasoning, that the angle DO X is equal to the angle I O X, and therefore F D must be the direction of the reflected ray. It can be shown in the same way that all the reflected rays proceed from F, which will thus be the focus of reflected rays. (Fig. 3.)

REFLECTION FROM CURVED SURFACES.-When a pencil of light is reflected from a curved mirror, each ray follows the ordinary laws of reflection. If three parallel rays, S A, 1 R, I' R', fall upon the concave mirror M N, the middle ray will be reflected in the same direction, A S, I R, and I' R', in the directions R F, R' F, so that the perpendiculars RO and R' O divide equally their angles of incidence and reflection. Every line drawn from o to the surface of the mirror is perpendicular to the mirror at that point. We see that, in order to make the angles of incidence and reflection equal, the parallel rays I R, I' R' must cross each other at a point, F, on the axis of the mirror. All other parallel rays cross at the same point. This point, F, is called the principal focus of the mirror. It can be proved by geometry that the distance, A F, of the principal focus from the mirror is equal to half the radius, A O, of the mirror. (Fig. 4.)

When the incident rays are not parallel to the axis of the mirror, but proceed from a point, Q, on its axis, F is no longer the focus, but some point, q, on the axis, whose position changes with that of Q. By making the angles of incidence and reflection equal, its position in every case can be fixed. It will be found on trial, that when Q lies between F and A, q will pass to the back of the mirror. The focus is then said to be virtual. A real image or focus is that formed by the reflected rays themselves, a virtual image or focus that formed by the prolongation of the reflected rays. In Figs. 4 and 5 we have examples of real foci, in Fig. 6 of a virtual focus. When the mirror is convex, as in this case, the focus is always virtual. It is necessary, to be able to find the distance of q from the mirror (focal length), which can be done by the following rule: multiply half the radius of the mirror by the distance of the incident rays from the mirror; divide the product by the difference of the distance of the incident rays and half the radius (if concave), and, if convex, divide by their sum. Example:-If the distance of incidental rays be 36 in.,

36X9

=

=12 in., or, if convex, 36

36X9.

36+9

and radius of mirror 18 in., focal length 7 in. IMAGES IN MIRRORS.-When an object is placed before a mirror, every point of the body sends out a pencil of light, which falls upon the mirror and is reflected. The foci of all the reflected rays form the image. The relative size of the image and object is proportional to their respective distances from the mirror if plane, or from the centre of the mirror if curved.

1. When the mirror is plane, as in Fig. 7, by the laws of reflection already stated, a is the focus of all the rays coming from A. Similarly, b is the focus of all the rays from B. Rays from all the points between A and B have their foci between a and b. Thus a complete image of A B is formed in a b. The

image is virtual, of the same size as the object, and at a distance behind the mirror equal to A B in front of it.

2. When the mirror is convex, the image will be placed as in Fig. 8, and is less than A B in the proportion bo to B O. It is here virtual.

3. When the mirror is concave (Fig. 9), and the object, A B, placed between the principal focus and the mirror, the image, a b, is virtual, erect, and enlarged in the proportion of bo to B O.

4. When the mirror is concave, and the object placed at a distance from the mirror greater than its focal length (Fig. 10), the image is real, inverted, and diminished. Conversely, if we suppose a b an object, A B will be the image, in this case real, inverted, and enlarged.

REFRACTION. If a ray of light, I 0, Fig. 11, fall obliquely on the surface of a dense medium, such as a plate of glass, A B, a portion of the ray is reflected in O R, and a portion transmitted. The transmitted portion, instead of going straight on in the direction O M, is bent towards the perpendicular to the surface in the direction O R'. This change in the path of the ray is termed refraction. It occurs when light passes from a rarer to a denser medium. In

the latter case the ray will be bent away from the perpendicular. Here, as in reflection, the angle of incidence, I O P, and the angle of refraction, R' O D, are in the same plane. Again, if a ray, 10, Fig. 12, fall upon the surface, A B, of a refracting medium, such as water, and points, N R, be taken in the incident and refracted rays at equal distances from O, the perpendiculars, N Q, R M, from these points on P M have a constant ratio for all angles of incidence. The ratio of A N to R M (RM) is called the index of refraction. The object in introducing a circle into the figure is to enable us to measure off equal distances, O N and O R.

Many facts of common observation receive an easy explanation from the law of refraction. Bodies placed in a medium more highly refracting than air appear nearer the surface of this medium than they really are. Let a body, c, be placed in a vessel of water, v, Fig. 13. A ray of light from C, on leaving the water, will be deflected from the perpendicular in the direction A R. The body will, therefore, be seen as if at c', the direction in which the ray is travelling when it enters the eye at R. It is for this reason that the eye is deceived with regard to the real depth of water. The rays of light appear to proceed from a point nearer the surface, and cause the bottom to appear more elevated than it really is. The index of refraction for water is, so that the eye is misled to the extent of one foot in every four; in other words, if water appear to the eye three feet deep, its real depth is four feet.

As long as the two surfaces of the refracting medium are parallel, the rays which pass through it emerge parallel to their original direction. The path of a ray of light through a triangular piece of glass, called a prism (Fig. 14), will

O DIIG G

FIG. 15.

B

FIG. 14.

FIG. 16.

show the altered direction of the ray when the faces of the medium are not parallel. The ray is always bent towards the thick part of the prism. A combination of surfaces may be so arranged as to cause all the refracted rays to converge towards one common line; such a combination forms a lens. A lens is a portion of any transparent medium adapted to magnifying purposes by having both surfaces spherical, or one spherical and the other plane. There are six forms of lens (Fig. 15). Those which are thickest at the centre are convex; those which are thinnest, concave. Rays passing through lenses are bent towards the thick part of the lens, so that the rays converge in a convex lens, and diverge in a concave. The focal length of lenses may be determined experimentally as follows: if convex (Fig. 16), expose the lens with its principal axis parallel to the sun's rays. By receiving upon a screen of polished glass the emergent pencil, we can easily ascertain the point where the rays converge. The distance of the lens from the screen is its focal length. In a concave lens the focal length may be found by projecting upon a screen the image of two points, a b, Fig. 17 (the rest of the surface being blackened). When the distance between the points in the image is double the distance a b on the lens, it is placed at its focal length.

The following consideration renders evident the use of a lens in magnifying objects. The apparent size of an object depends upon its distance from the If. then, an object could be brought indefinitely near the eye, its apparent size might be increased to any extent. It is found, however, that objects brought nearer to the eye than a certain distance, which varies with different

eye.