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Refraction by Lenses

Refraction by Lenses

Refraction by lenses is somewhat more complicated. A lens is an optical contrivance usually made of glass, and consists of a refracting medium with two opposite surfaces, one or both of which may be segments of a sphere; they are then called spherical
lenses, of which there are six varieties.

1. Plano-convex, the segment of one sphere (Fig.
11, B)

2. Biconvex, segments of two spheres (Fig. 11, A)

3. Converging concavo-convex, also called a converging meniscus

4. Plano-concave

5. Biconcave

6. Diverging concavo convex, called also a diverging meniscus

Lenses may be looked upon as made up of a number of prisms with different refracting angles. Convex lenses, made up of prisms placed with their bases together and concave lenses, made up of prisms with their edges together.

A ray passing from a less refracting medium (as air) through a lens, is deviated towards the thickest; part, therefore the first three lenses, which are thickest at the centre, are called converging ; and the others, which are thickest at the borders, diverging.

A line passing through the centre of the lens, called the optical centre at right angles to the surfaces of the lens, is termed the principal axis, and any ray passing through that axis is not refracted. All other rays undergo more or less refraction.

Rays passing through the optical centre of it lens, but not through the principal axis, suffer slight deviation, but emerge in the same direction as they entered ; the deviation in thin lenses is so slight that they are usually assumed to pass through in a straight line, and are called secondary axes (Fig. 13).

Parallel rays falling on a bicolivex lens are rendered convergent; thus in Fig. 14 the rays A, B, C, strike the surface of the lens (L.) at the points D, E, F; the centre ray (B) falls on the lens at E perpendicular to its surface, and therefore passes through in a
6traight line ; it also emerges f ral the lens at right angles to its opposite surface, and so continues its course without without deviation; but the ray (A) strikes the surface of the lens obliquely at D, and as the ray is passing from one medium (air) to another (glass)
FIG. 13.
which is of greater density, it is bent towards the perpendicular of the surface of the lens, shown by the dotted line M K ; the ray after deviation passes through the lens, striking its opposite surface obliquely
Fig. 14.
at O, and as it leaves the lens, enters the rarer medium (air), being deflected from the perpendicular N O ; it is now directed to H,where it meets the central ray B H ; ray C, after undergoing similar refractions, meets the other rays at H, and so also all parallel rays falling on the biconvex lens (L).

Parallel rays, therefore, passing through a convex lens (L) are brought to a focus at a certain fixed point (A) beyond the lens; this point is called the principal focus, and the distance of this focus from the lens is called the focal length of the lens.
Rays from a luminous point placed at the principal focus (A) emerge as parallel after passing through the lens.

Divergent rays from a point (B) outside the princ1pal focus (F, Fig; 16) meet at a distance beyond (F') the principal focus on the other side of the lens (L), and if the distance of the luminous point (B) is equal to twice the focal length of the lens, the rays will focus at a point (C) the same distance on the opposite side of the lens; rays coming from C would also focus at n; they are therefore oalled conjugate foci, for we can indifferently replace the image (C) by the object (B) and the object (B) ty the image (C).

If the luminous point (D) be between the lens and the principal focus (F), then the rays will issue from the lens divergent, though less so than before entering it; and if we prolong them backwards they will meet at a point (H) further from the lens than the
point D ; H will therefore be the virtual focus of D, and
the conjugate focus of D may be spoken of as negative.

Biconvex lenses have therefore two principal foci, F and F', one on either side, at an equal distance from the centre.

In ordinary lenses, and those in which the radii of the two surfaces are nearly equal, the principal focus closely coincides with the centre of curvature.

We have assumed the luminous point to be situated on the principal agi-s, supposing, however, it be to one side of it as at E (Fig. 17), then the line (E F) passing through the optical centre (C) of the lens (L) is a secondary axis, and the focus of the point E will be found somewhere on this line, say at F, so that what has been said respecting the focus of a luminous point on the principal axis (A B) is equally true for points on a secondary axis, provided always that the inclination of this secondary axis is not too great, when the focus would become imperfect on account of the spherical aberration which would be produced.

FiG. 17.

In biconcave lenses the foci are always virtual whatever the distance of the object. Rays of light parallel to the axis diverge after refraction, and if their direction be continued backward they will meet at a point termed the principal focus (Fig. 18, F).

Fig. 19 shows the refraction of parallel rays by a biconcave lens (L) ; the centre ray B strikes the lens at E perpendicular to its surface, passing through without refraction, and as it emerges from the opposite side of the lens perpendicular to its surface, it continues in a straight line ; the ray A strikes the lens
obliquely at D and is refracted towards the perpendicular, shown by the dotted line G H ; the ray after
FIG. 19.
deviation passes through the lens to K, where, on entering the medium of less density obliquely, it is refracted from the perpendicular O P, in the direction K M ; the same takes place with ray C at F and N ; so also with all intermediate parallel rays.

Formation of Images. To illustrate the formation of images the following simple experiment may be carried out: Place on one side of a screen having a small perforation, a candle, and on the other side of the screen a sheet of white cardboard at some distance from it to receive the image formed; rays diverge from the candle in all directions, most of those falling on the screen are intercepted by it, but some few rays pass through the petforation and form an image of the candle on the cardboard, the image being inverted because the rays cross each other at the orifice.

It can further be shown that when the candle and cardboard are equally distant from the perforated screen, the candle flame and its image will be of the same size. If the cardboard be moved further from the screen the image is enlarged, if it be moved nearer it is diminished; if we make a dozen more perforations in the screen, a dozen more images will be formed on the cardboard, if a hundred then a hundred ; but if the apertures come so close together that the images overlap, then instead of so many distinct images we get a general illumination of the cardboard.

The image of an object is the collection of the foci of its several points; the images formed by lenses are, as in the case of the foci, real or virtual. Images formed, therefore, by convex Ienses may be real or virtual.

In Fig. 21, let A B be a candle. situated at an infinite distance; from. the extremities of A B draw two lines passing through the optical centre (C) of a bicorlvex lens, then the image of A will be formed somewhere on the line A c (termed a secondary axis),
say at a ; the image of B will be formed on the line B c b, say at b; therefore b a is a small inverted image of the candle A B, formed at the principle focus of the convex lens. Had the candle been placed at twice the focal distance of the lens, then its inverted image would be formed at a corresponding point on the opposite site of the lense, and would be of the same size as the subject.

If the candle be at the principal focus (F), then the image is at an infinite distance, the rays after refraction being parallel.

If, however, the candle (A B) be nearer the lens than the focus, then the rays which diverge from the candle will, after passing through the conves lens, be still divergent, so that no image is formed; an eye placed at E would receive the rays from A B as is they came from a b; a b is therefore a virtual image of A B, erect
and larger than the object, and formed on the same side of the lens as the object.

Images formed by biconcave lenses are always virtual, erect, and smaller than the object. Let A B a candle, and F the principal focus of a biconcave lens; draw from A B two lines through C, the optical centre of the lens, and lines also from A and B parallel to the
axis; after passing through the lens they diverge and have the appearance of coming from a b, which is therefore the virtual image of A B. A real image can be projected on to a screen, but a
virtual one can only be seen by looking through the
lens.