A knowledge of the ordinary principles of optics on the part of the reader is a.s.sumed, for there are plenty of books on the theory of lenses, and, in any case, it is my intention to treat of the art rather than of the science of the subject. By far the best short statement of the principles involved which I have seen is Lord Rayleigh's article on Optics in the Encyclopaedia Britannica, and this is amply sufficient.

The first question that crops up is, of course, the subject of the choice of gla.s.s. It is obvious that the gla.s.s must be uniform in refractive index throughout, and that it must be free from air bubbles or bits of opaque matter. [Footnote: The complete testing of gla.s.s for uniformity of refractive index can only be arrived at by grinding and polishing a sufficient portion of the surfaces to enable an examination to be made of every part. In the case of a small disc it is sufficient to polish two or three facets on the edge, and to examine the gla.s.s in a field of uniform illumination through the windows thus formed. Very slight irregularities will cause a "mirage"

easily recognised.]

The simplest procedure is to obtain gla.s.s of the desired quality from Messrs. Chance of Birmingham, according to the following abbreviated list of names and refractive indices, which may be relied upon:-

Density. Refractive Index.

C D F G

Hard crown

2.85 1.5146 1.5172 1.5232 1.5280

Soft crown

2.55 1.5119 1.5146 1.5210 1.5263

Light flint

3.21 1.5700 1.5740 1.5839 1.5922

Dense flint

3.66 1 6175 1.6224 1.6348 1.6453

Extra dense flint

3.85 1.6450 1.6504 1.6643 1.6761

Double extra dense flint

4.45 1.7036 1.7103 1.7273 ...

The above gla.s.ses may be had in sheets from 0.25 to 1 inch thick, and 6 to 12 inches square, at a cost of, say, 7s. 6d. per pound.

Discs can also be obtained of any reasonable size. Discs 2 inches in diameter cost about 1 per dozen, discs 3 inches in diameter about 10s. each. The price of discs increases enormously with the size. A 16-inch disc will cost about 100.

For special purposes, where the desired quality of gla.s.s does not appear on the list, an application may be made to the Jena Factory of Herr Schott. In order to give a definite example, I may mention that for ordinary telescopic objectives good results may be obtained by combining the hard crown and dense flint of Chance's list, using the crown to form a double convex, and the flint to form a double concave lens. The convex lens is placed in the more outward position in the telescope, i.e. the light pa.s.ses first through it.

The conditions to be fulfilled are:

(1) The gla.s.s must be achromatic;

(2) it must have a small spherical aberration for rays converging to the princ.i.p.al focus.

It is impossible to discuss these matters without going into a complete optical discussion. The radii of curvature of the surfaces, beginning with the first, i.e. the external face of the convex lens, are in the ratio of 1, 2, and 3; an allowance of 15 inches focal length per inch of aperture is reasonable (see Optics in Ency.

Brit.), and the focal length is the same as the greatest radius of curvature. Thus, for an object gla.s.s 2 inches in diameter, the first surface of the convex lens would have a radius of curvature of 10 inches, the surface common to the convex and concave lens would have a radius of curvature of 20 inches, and the last surface a radius of curvature of 30 inches. This would also be about the focal length of the finished lens. The surfaces in contact have, of course, a common curvature, and need not be cemented together unless a slight loss of light is inadmissible.

I will a.s.sume that a lens of about 2 inches diameter is to be made by hand, i.e. without the help of a special grinding or polishing machine; this can be accomplished perfectly well, so long as the diameter of the gla.s.s is not above about 6 inches, after which the labour is rather too severe. The two gla.s.s discs having been obtained from the makers, it will be found that they are slightly larger in diameter than the quoted size, something having been left for the waste of working.

It is difficult to deal with the processes of lens manufacture without entering at every stage into rather tedious details, and, what is worse, without interrupting the main account for the purpose of describing subsidiary instruments or processes. In order that the reader may have some guide in threading the maze, it is necessary that he should commence with a clear idea of the broad principles of construction which are to be carried out. For this purpose it seems desirable to begin by roughly indicating the various steps which are to be taken.

(1) The gla.s.s is to be made circular in form and of a given diameter.

(2) Called Rough Grinding. The surfaces of the gla.s.s are to be made roughly convex, plane, or concave, as may be required; the gla.s.s is to be equally thick all round the edge. In this process the gla.s.s is abraded by the use of sand or emery rubbed over it by properly shaped pieces of iron or lead called "tools."

(3) The gla.s.s is ground with emery to the correct spherical figure as given by a spherometer.

(4) Called Fine Grinding. The state of the surface is gradually improved by grinding with finer and finer grades of emery.

(5) The gla.s.s is polished by rouge.

(6) The gla.s.s is "figured." This means that it is gradually altered in form by a polishing tool till it gives the best results as found by trial.

In processes 2 to 5 counterpart tool surfaces are required--as a rule two convex and two concave surfaces for each lens surface. These subsidiary surfaces are worked (i.e. ground) on discs of cast iron faced with gla.s.s, or on slate discs; and discs thus prepared are called "tools."

Taking these processes in the order named, the mode of manufacture is shortly as follows:-

(1) The disc of gla.s.s, obtained in a roughly circular form, is mounted on an ordinary lathe, being conveniently cemented by Regnault's mastic to a small face plate. The lathe is rotated slowly, and the gla.s.s is gradually turned down to a circular figure by means (1) of a tool with a diamond point; or (2) an ordinary hand-file moistened with kerosene, as described in -- 42; or (3) a ma.s.s of bra.s.s or iron served with a mixture of emery--or sand--and water fed on to the disc, so that the disc is gradually ground circular.

The operation of making a circular disc of given diameter does not differ in any important particular from the similar operation in the case of bra.s.s or iron, and is in fact merely a matter of turning at a slow speed.

(2 and 3) Roughing or bringing the surfaces of the gla.s.s roughly to the proper convex or concave shape. This is accomplished by grinding, generally with sand in large works, or with emery in the laboratory, where the time saved is of more importance than the value of the emery.

Discs of iron or bra.s.s are cast and turned so as to have a diameter slightly less than that of the gla.s.s to be ground, and are, say, half an inch thick. These discs are turned convex or concave on one face according as they are to be employed in the production of concave or convex gla.s.s surfaces. The proper degree of convexity or concavity may be approximated to by turning with ordinary turning tools, using a circular arc cut from zinc or gla.s.s (as will be described) as a "template" or pattern. This also is a mere matter of turning.

The first approximation to the desired convex or concave surface of the gla.s.s is attained (in the case of small lenses, say up to three inches diameter) by rotating the gla.s.s on the lathe as described above (for the purpose of giving it a circular edge) and holding the tool against the rotating gla.s.s, a plentiful supply of coa.r.s.e emery and water, or sand and water, being supplied between the gla.s.s and metal surfaces. The tool is held by hand against the surface of the revolving gla.s.s, and is constantly moved about, both round its own axis of figure and to and fro across the gla.s.s surface. In this way the gla.s.s gradually gets convex or concave.

The curvature is tested from time to time by a spherometer, and the tool is increased or decreased in curvature by turning it on a lathe so as to cause it to grind the gla.s.s more at the edges or in the middle according to the indications of the spherometer.

This instrument, by the way--so important for lens makers--consists essentially of a kind of three-legged stool, with an additional leg placed at the centre of the circle circ.u.mscribing the other three.

This central leg is in reality a fine screw with a very large head graduated on the edge, so that it is easy to compute the fractions of a turn given to the screw. The instrument is first placed on a flat plate, and the central screw turned till its end just touches the plate, a state of affairs which is very sharply discernible by the slight rocking which it enables the instrument to undergo when pushed by the hand. See the sketch.

On a convex or concave surface the screw has to be screwed in or out, and from the amount of s.c.r.e.w.i.n.g necessary to bring all four points into equal contact, the curvature may be ascertained.

Let a be the distance between the equidistant feet, and d the distance through which the screw is protruded or retracted from its zero position on a flat surface. Then the radius of curvature rho is given by the formula 2rho = a2/3d +d.

Fig. 43.

The process of roughing is not always carried out exactly as described, and will be referred to again.

(4) The gla.s.s being approximately of the proper radius of curvature on one side, it is reversed on the chuck and the same process gone through on the other side. After this the gla.s.s is usually dismounted from the lathe and mounted by cement on a pedestal, which is merely a wooden stand with a heavy foot, so that the gla.s.s may be held conveniently for the workman. Sometimes a pedestal about four feet high is fixed in the floor of the room, so that the workman engaged in grinding the lens may walk round and round it to secure uniformity.

For ordinary purposes, however, a short pedestal may be placed on a table and rotated from time to time by hand, the operator sitting down to his work.

Rough iron or bra.s.s tools do not succeed for fine grinding--i.e.

grinding with fine emery, because particles of emery become embedded in the metal so tightly that they cannot be got out by any ordinary cleaning. If we have been using emery pa.s.sing say a sieve with 60 threads to the inch, and then go on to some pa.s.sing say 100 threads to the inch, a few of the coa.r.s.er particles will adhere to the "tool", and go on cutting and scratching all the time grinding by means of the finer emery is in progress.

To get over this it is usual to use a rather different kind of grinding tool. A very good kind is made by cementing small squares of gla.s.s (say up to half an inch on the side), on to a disc of slate slightly smaller than the lens surface to be formed (Fig. 51). The gla.s.s-slate tool is then "roughed" just like the lens surface, but, of course, if the lens has been roughed "convex" the tool must be roughed "concave".