and C D a ray of light incident upon it.

B

E

It will be

Fig. 48.

refracted in passing through the glass, and again on emerging in the direction of the line E F, parallel to CD. Hence, in looking through a window, if it has good glass we do not see the position of objects changed.

If the bounding surfaces of the medium through which light passes be not parallel, the direction of every ray passing through it is permanently altered, and the greater the inclination of the two surfaces, the greater the alteration.

A Prism.-In optics a prism is a transparent medium enclosed between two plane faces inclined at an angle towards each other. On looking through a prism all objects appear removed from their true position. Let C A B (Fig. 49) be a section of a prism, and ac a ray of light incident on it. In passing through the prism it will be refracted towards the normal, or in the direction of the base of the prism, because glass is more refracting than air. Again, on

emerging it will be refracted from the normal, i. e., towards the thickest part of the prism, becauses it passes into a less refractive medium, and will take the direction from g to the eye; and as objects always appear in the direction in which the last ray enters the eye, the object a will appear at f—that is, objects seen through a prism appear deflected towards its summit. It will also be shown in speaking of colour that objects seen through a prism appear in all the colours of the rainbow.

Lenses.-A lens is a refracting medium bounded by curved surfaces, or by one curved and one plane surface. Lenses are usually made of glass. There are six kinds of lenses, named according to the nature of the bounding surfaces.

1

Fig. 50.

I is a double convex lens, bounded by two convex surfaces. When the curvature of the two surfaces is the same, the lens is said to be equally convex. 2 is a plano-convex lens. 3 is a double concave lens. 4 is a plano-concave lens.

is a converging meniscus 6 is a diverging meniscus

both concavo-convex.

Nos. 1, 2, and 5 are thicker in the centre than at the edges. These collect the rays of light, and are convergent lenses. Nos. 3, 4, and 6 thinner in the middle, and are named divergent lenses. The centres of the bounding surfaces of a lens are the centres of curvature, and straight lines through the centres of curvature are called the principal axes of the lenses.

Spherical lenses are used in optics. They are made of crown or flint glass, the latter containing more lead and being more refractive. It has already been stated that rays of light passing through a prism are deflected towards its base, and if we imagine that in lenses 1, 2, and 5 the summits are outwards, and in 3, 4, and 6 inwards, as in Fig. 51; we then see that the first three condense the rays while the others disperse them.

Fig. 51.

Fig. 52.

When a ray of light enters a prism, it does not follow that it will always be refracted. It may be totally reflected, as in Fig. 52, where the ray enters the glass at such an angle as to be refracted on entering; but on arriving at the opposite surface it strikes at an angle which is beyond the critical angle for glass into air (41° 48'). Therefore it cannot pass, but is totally reflected in direction a b.

Action of Lenses.-In explaining the action of lenses on light, it is only necessary to take the double convex and double concave lenses, as the others are only modifications of them, and have the same effects, only in a different degree.

It will be well to recall what has been said about concave mirrors and their foci here, for double convex lenses have the same foci, real and virtual.

F

Fig. 53.

Case 1.-Let us suppose that the luminous rays are parallel, they will on passing through the lens be twice refracted towards the normal, as at a and b of the ray Sa. All the other rays are similarly refracted, and cut the principal axis in F, which is the principal focus. FA is the principal focal distance when the angle of aperture is not above 10° or 12°. With the same lens the focus is at the same distance, but varies with the refractive power of the glass and the curvature of the lens.

Case 2.-Let the rays emanate from a point sufficiently near to form a pencil of rays. Fig. 54.

It will be readily seen that ray Sa makes with normal a F a greater angle than ray N a, consequently when the second refraction takes place the latter ray emerges higher, and will be focussed at a point e beyond the principal focus: e is the conjugate focus of N, for all rays proceeding from N will find their focus at this point. Case 3.-If the light be placed at e the focus will be at N. The word conjugate refers to this relation between them.

Fig. 54.

If N be moved nearer the lens, focus e moves further away, until (Case 4) when N is placed at the centre of curvature the rays emerge on the opposite side in parallel lines, and there is no focus.

Case 5.-Let N be placed between the principal focus and the lens. Fig. 55. Then its rays will be twice refracted, and emerge at an angle Src much larger than the angle p r c, produced with the normal by the ray from the principal focus; and as that was parallel this is divergent, and to obtain its focus we must continue it backwards to the same side of the lens as N to the point V, which of course, being on the same side as N, will be a virtual focus.

p

S

Fig. 55.

Case 6.-In concave lenses there are only virtual foci, whatever the distance of the object. In Fig. 56 let pr represent a parallel ray. It is twice refracted and emerges as part of a divergent pencil, the focus of which is at F. It will form a useful exercise to vary the position of the light, and to draw diagrams to show the different foci. The student will find no