the prism at E is refracted towards the normal and travels through the prism in the direction EE'. On leaving the prism at E' the ray is passing from a denser to a rarer medium hence it is refracted away from the normal along E'D'. Thus, in our figure, the ray at each refraction is turned away from the edge of the prism or towards its base.

Produce DE and D'E' to meet. The angle FGD' is called the angle of deviation: it is the angle between the directions of the incident and emergent rays, and measures the total deviation produced by the prism. The deviation is always away from the edge of the prism.

The glass pendants attached to chandeliers are usually triangular prisms, and can be used for illustrating the behaviour of prisms. The effect of interposing a prism between your eye and an object is to shift the apparent position of the object towards the edge of the prism. Thus an observer at D (Fig. 58), looking through a prism at an object D', would see a virtual image of it at F.

58. Minimum Deviation, etc.-The deviation produced by a prism depends not only upon its angle and refractive index, but also upon its position with reference to the direction of the incident light. It can be proved that the deviation is least (or a minimum) when the angles of incidence and emergence are equal. When this is the case, the path of the ray within the prism is equally inclined to the two faces (as in Fig. 58), and the position of the prism in which this occurs is called the 'position of minimum deviation.' This is the position in which prisms are usually placed in optical experiments.

In the case of prisms of small angle (say up to 15°) the deviation is approximately proportional to the angle of the prism. This should be borne in mind when we come to consider how a lens acts (Art. 63).

EXPT. 35.-On a table or drawing-board place a prism with its edge vertical. Beyond the prism stick a pin (to represent a source of light). Look through the prism and note the apparent position of the pin; this depends upon the position of the prism. Twist the prism slightly, first in one direction and then in the other: find by trial the position in which the deviation is a minimum.

By using four pins-two on one side of the prism and two on the other -you can fix the directions of the incident and emergent rays and then measure the deviation. (When the pins are properly adjusted they should all appear to be in a straight line.) Do this with two prisms of the same angle but of different materials, and observe that the deviations are different e.g. a prism of flint-glass produces a greater deviation than one of crown.

59. Objects seen through prisms generally exhibit coloured edges: the cause of this will be explained in Chap. VIII.

Several of the experiments described in the present chapter are suitable for projection with the lantern, e.g. Expts. 31-34.

The effect of heat in altering the refractive index of liquids and gases has been referred to in pp. 90 and 93.

EXAMPLES ON CHAPTER VI

1. Explain the apparent bending of a stick when dipped into water, stating broadly from experience the most favourable conditions for observing the effect.

2. Light falls at a given angle on a plane refracting surface, for which the refractive index is 5/4. Show, by a geometrical construction, drawn, as well as you can, to scale, how to find the path of the refracted ray. (Apply the construction given in Art. 46.)

3. A ray of light passes from one medium into a second, the angle of incidence being 60°, and the angle of refraction 30°: show that the index of refraction is √3.

4. The critical angle for a certain medium is 45°: show that its index of refraction is √2. (See Art. 49.)

5. Draw accurately the path of a ray of simple light through a 45° prism of glass, whose index of refraction is 5; drawing the ray incident on one face in a direction perpendicular to the other face.

6. The shadow of a red-hot poker is cast on a white screen by means of a lime-light lantern. Explain the smoky appearance on the screen just above the shadow.

7. Explain the quivery appearance seen above hot bricks or rocks, and the streaky appearance of water in which ice or sugar is being dissolved.

CHAPTER VII

LENSES

60. A lens is a portion of a refracting medium bounded either by two curved surfaces or by one plane surface and one curved surface. The only lenses which we shall consider are glass lenses of which the curved surfaces are portions of spheres. We shall further assume that the greatest thickness of the lens is small compared with the radii of curvature of the surfaces.

61. Kinds of Lenses.-Lenses may be divided into two classes:

I. Those which are thicker at the centre than at the edge. These are called convex or converging lenses. Sections

of three lenses of this kind are shown in Fig. 59. Of these A has two convex surfaces and is called a double-convex lens ; B has one plane and one convex surface and is called a planoconvex lens; while C is called a converging meniscus.

II. Those which are thinner at the centre than at the edge. These are called concave or diverging lenses. Three lenses of this kind are shown in Fig. 60. Of these D is a double concave and E a plano-concave lens, while F is a diverging meniscus.

62. The principal axis of a lens is the line joining the centres of curvature of its two spherical surfaces. The axis of a plano-convex or plano-concave lens is the line which passes through the centre of curvature of the spherical surface and is perpendicular to the plane surface.

A ray of light travelling along the axis of a lens falls normally on both refracting surfaces, and therefore passes through the lens without suffering any deviation.

63. How a Lens Acts.—In any convex lens the inclination of the two faces towards one another increases as we go out

Fig. 61.

wards from the centre (or axis) of the lens towards the edge. Thus we may imagine the section of the lens to be made up of a number of prisms of gradually increasing angle, as shown in the accompanying diagram.

We know that a ray of light in passing through a prism is deviated towards its base, and that the amount of the deviation increases as the angle of the prism increases. Now suppose a beam of parallel rays to fall upon the prismlens, shown in Fig. 61. The rays would be bent towards the axis, those near the edge being deviated more than those nearer the centre. The result

would be to convert the parallel beam into a convergent pencil.

Their general

This is the way in which convex lenses act. effect is to render transmitted rays more convergent.

The section of a concave lens may be regarded as being built up of a number of prisms of gradually-increasing angle, arranged with their bases outwards (or away from the centre). The general effect of such lenses is to render transmitted rays more divergent.

Thus the properties of convex lenses are similar to those of concave mirrors; while the properties of concave lenses are similar to those of convex mirrors.

64. Optical Centre of a Lens.-The axis is not the only direction in which a ray of light can pass through a lens without suffering deviation. There is one point on the axis of every lens such that, if the path of a ray within the lens passes through this point, the emergent ray is parallel to the incident ray. This point is called the optical centre of the lens, and any line passing through it is called a secondary axis of the lens. In the two accompanying diagrams of convex and concave lenses O is the optical centre, and the line IOI' is a secondary axis. At the points I and I' where this line meets the lens its two surfaces are parallel to one another, and consequently the lens acts upon a ray traversing it in this direction just as if it were a parallel-sided plate: the ray emerges parallel to its direction before incidence, but suffers a slight lateral displacement

(Art. 54).

N

not necessarily the geometrical centre: indeed in the case of a meniscus it may be altogether outside the lens. But in the common types of lenses shown in Fig. 62 (double-convex and doubleconcave lenses with surfaces of equal curvature) the optical centre does coincide with the geometrical centre, or is midway between the points A and B.

O