object O and falling upon the horizontal mirror CM appear, after reflection, to proceed from the primary image 11. Some of these rays fall upon the vertical mirror CM'. I, lies in front of this mirror, and may be regarded as a virtual object sending out rays of light which, after a second reflection (from CM'), appear to diverge from the point I2, which is as far behind the vertical mirror as I, is in front of it. 12 is a secondary image of O produced by successive reflections from the horizontal and vertical mirrors.

I may be regarded as consisting of two coincident secondary images. For by a single reflection at the vertical mirror a primary image is produced at I. This is in front of the horizontal mirror, and hence, as already described, a secondary image would be produced at a point as far behind the horizontal mirror as I' is in front of it. But it is clear from the figure that this secondary image would coincide in position with I2.

24. Parallel Mirrors-EXPT. 15.-Stand two mirrors vertically on a table and facing one another. Between them place a candle or other object. Look over the edge of one mirror into the other. You see a large number of images, and if the mirrors are exactly parallel, these images lie all in a straight line. They are produced by repeated reflections of light from one mirror to the other until the light reaches the eye. Good examples of these multiple images can often be seen in shops and restaurants where mirrors are fixed to opposite walls.

The positions of these images and the paths of the rays can be easily determined as in the last article. Rays of light proceeding from an object O (Fig. 25) and falling on the mirror M appear, after reflection, to proceed from the primary image I1. If these rays fall upon the mirror M', and are again reflected, they appear to come from a point I2, which is as far behind M' as I, is in front of it. I is a secondary image of I. In the same way, a single reflection from M' produces a primary image at I, and a second reflection from M gives a secondary image at I. The

tertiary images I and I,' are produced by three successive reflections (two from one mirror and one from the other). All the images lie on the straight line through O perpendicular to the mirrors. Each pair of images gives rise to another pair, for every image is in front of one or other of the mirrors. Thus in theory there should be an infinite

number of images: but in practice it is found that the light is so much weakened by successive reflections that beyond a certain point the images are no longer visible.

25. Images are produced not only by reflection from silvered glass but also by other reflecting surfaces, such as still water and unsilvered glass. As you walk past shop windows you see images of yourself and of other objects by reflection from the window-glass. Since the glass is transparent, you can at the same time see the contents of the shop-window. This is the principle upon which "" 'Pepper's Ghost" and other optical illusions depend.

EXPT. 17.-Hold the point of a pencil against a sheet of thick plate

glass and look at it sideways. Several images are seen.

Fig. 26.

The first of these

(the one which touches the pencil point) is produced by reflection from the front surface of the glass. The second is produced by reflection

L

from the back surface. The others are produced by repeated reflections between the front and back surfaces.

Repeat the experiment with a candle, light falls on it obliquely, as in Fig. 27.

holding the glass so that the If a plate-glass mirror is used

instead of a piece of unsilvered glass, the second image (that produced by reflection from the back or silvered surface) will be the brightest, as shown in the figure.

EXAMPLES ON CHAPTER IV

1. When a horizontal beam of light falls on a vertical plane mirror which revolves about a vertical axis in its plane, show that the reflected beam revolves at twice the rate of the mirror.

means.

2. Distinguish between a real and virtual image formed by optical A candle is placed in front of a piece of flat glass, and on looking into the glass an image of the candle is seen: show how to determine the position of this image. Is it real or virtual?

3. Describe and explain the difference of the effects observed when the sun sets over a smooth lake or sea, according as the water is (1) absolutely smooth, or (2) covered with ripples.

4. A source of light is seen by reflection in two vertical plane mirrors placed against the two walls in a corner of a square room. Construct a figure showing exactly the path of a beam which enters the eye of an observer after two reflections, one at each mirror.

5. A candle is placed at a given small distance in front of an ordinary looking-glass made of thick plate-glass quick-silvered on the back, and a person looking obliquely into the mirror sees several images of the candle : explain this, and show the exact positions of the images by a diagram.

6. A ray of light is reflected successively from two mirrors inclined at right angles to each other (as in Fig. 24). Prove that the ray after a second reflection is parallel to its original direction.

7. Prove that if an object in front of a plane mirror moves through a distance d away from the mirror, the image will move through the same distance; whereas if the mirror moves parallel to itself through a distance d (the object remaining fixed) the image will move through a distance 2d.

CHAPTER V

SPHERICAL MIRRORS

26. Definitions.-A spherical mirror is a portion of a spherical reflecting surface. The centre of curvature of the mirror is the centre of the sphere of which the mirror forms a part. The radius of the sphere is called the radius of curvature of the mirror. Spherical mirrors may be either concave or convex. In concave mirrors the reflection takes place from the inner face (that which faces towards the centre of curvature). In convex mirrors the reflection takes place from the outer face (that which faces away from the centre of curvature). Fig. 28 represents a section of a concave spherical mirror of which is the centre of curvature.

M

M'

Fig. 28.

MM' is called the diameter or aperture of the mirror; the angle McM', included between the lines Mc and M'c, is called the angular aperture of the mirror. The centre of the face of the mirror is at d. This point is sometimes called simply the centre of the mirror. This, however, might leave us

in doubt as to whether c or d was referred to. We shall, therefore, call the point d the vertex or pole of the mirror. The distance cd is the radius of curvature.