Applied Optics:—Eye-pieces; Achromatic Objectives; Condensers.
It is almost unnecessary to say that the eye-piece forms a most important part of applied optics in the microscope. It is an optical combination designed to bring the pencil of rays from the objective to assist in the formation of a real or virtual image before it arrives at the eye of the observer. Greater attention has been given of late years to the improvement of the eye-piece, since flatness of field much depends upon it. Opticians have therefore sought to make it both achromatic and compensatory.
There are several forms of eye-pieces in use, some of which partake of a special character, and these will receive attention in their proper places. It is, however, customary among English opticians to denote the value of their several eye-pieces by Roman capitals, A, B, C, D, and E. Continental opticians, on the other hand, have a preference for numerals, 1, 2, 3, 4, 5 and 6, or more, and by which they are recognised.
The eye-piece in more general use is that known as the Huyghenian ([Fig. 99]); this came into use upwards of two centuries ago. It was constructed by Christian Huyghens, a Dutch philosopher and eminent man of science, secretary to William III.
It was made for the eye-piece of a telescope he constructed with his own hands, and it has been in constant use as the eye-piece of the microscope for nearly two centuries. It consists of two plano-convex lenses, with their plane surfaces turned towards the eye, and divided at a distance equal to half the sum of their focal lengths—in other words, at half the sum of the focal length of the eye-glass and of the distance from the field-glass at which an image from the object glass would be formed, a stop, or diaphragm, being placed between the two lenses for the reason about to be explained. Huyghens himself appears to have been quite unaware of the value of an eye-piece so cleverly constructed.
Fig. 99.—Huyghenian Eye-piece A, the dotted lines show position of lenses.
It was reserved for Boscovich to point out that, by this important arrangement, he had corrected a portion of the chromatic aberration incidental to the earlier form of eye-pieces. Let [Fig. 100] represent the Huyghenian eye-piece of a microscope, f f being the field-glass, and e e the eye-glass, and l m n the two extreme rays of each of the three pencils emanating from the centre and ends of the object, of which, but for the field-glass, a series of coloured images would be formed from r r to b b; those near r r being red, those near b b blue, and the intermediate ones green, yellow, and so on, corresponding with the colours of the prismatic Spectrum.
The effect described, that of projecting the blue image beyond the red, over-correcting the object-glass as to colour, is purposely produced; it is also seen that the images b b and r r are curved in the wrong direction to be seen distinctly by the convex eye-lens; this then is a further defect of the compound microscope made up of two lenses. But the field-glass, at the same time that it bends the rays and converges them to foci at b′ b′ and r′ r′, also reverses the curvature of the images as here shown, giving them the form best adapted for distinct vision by the eye-glass e e. The field-glass has at the same time brought the blue and red images closer together, so that they produce an almost colourless image to the eye. The chromatic aberration of lenses has been clearly explained in a previous chapter. But let it be supposed that the object-glass had not been over-corrected, that it had been perfectly achromatic; the rays would then have appeared coloured as soon as they had passed the field-glass; the blue rays of the central pencil, for example, would converge at b′′, and the red rays at r′′, which is just the reverse of what is required of the eye-lens; for as its blue focus is also shorter than its red, it would require that the blue image should be at r′′, and the red at b′′. This effect is due to over-correction of the object-glass, which removes the blue foci b b as much beyond the red foci r r as the sum of the distances between the red and the blue foci of the field-lens and eye-lens; so that the separation b r is exactly taken up in passing through those two lenses, and the several colours coincide, so far as focal distance is concerned, as the rays pass the eye-lens. So that while they coincide as to distance, they differ in another respect—the blue image is rendered smaller than the red by the greater refractive power of the field-glass upon the former. In tracing the pencil l, for instance, it will be noticed that, after passing the field-glass, two sets of lines are drawn, one whole and one dotted, the former representing the red, and the latter the blue rays. This accidental effect in the Huyghenian eye-piece was pointed out by Boscovich. The separation into colours of the field-glass is like the over-correction of the object-glass—and opens the way to its complete correction. If the differently-coloured rays were kept together till they reached the eye-glass, they would still be coloured, and present coloured images to the eye. The separating effected by the field-glass causes the blue rays to fall so much nearer the centre of the eye-glass, where, owing to its spherical figure, the refractive power is less than at the margin, so that spherical error of the eye-lens may be said to constitute a nearly equal balance to the chromatic dispersion of the field-lens, and the blue and red rays l′ and l′′ emerge nearly parallel, presenting a fairly good definition of a single point to the eye. The same may be said of the intermediate colours of the other pencils. The eye-glass thus constructed not only brings together the images b′ b′, r′ r′, but it likewise has the most important effect of rendering them flatter, and assisting in the correction of chromatic and spherical aberration.
Fig. 100.—Huyghenian Eye-piece.
Fig. 101.—Ramsden’s Eye-piece.
The later form of the Huyghenian eye-piece is that of the late Sir George Airy, the field-glass of which is a meniscus with the convex side turned towards the objective, and the eye-lens a crossed convex with its flatter side towards the eye. Another negative eye-piece is that known as the Kellner, or orthoscopic eye-piece. It consists of a bi-convex field-glass and an achromatic doublet eye-lens. This magnifies ten times, but it in no way compares with the Huyghenian in value. Neither does it afford the same flatness of field.
The Ramsden, or positive eye-piece, is chiefly employed as a micrometer eye-piece for the measurement of the values of magnified images. The construction of this eye-piece is shown in [Fig. 101], a divided scale being cut on a strip of glass in 1⁄100ths of an inch, every fifth of which is cut longer than the rest to facilitate the reading of the markings, and at the same time that of the image of the object, both being distinctly seen together, as in the accompanying reduced micro-photograph of blood corpuscles, [Fig. 102].
The value of such measurements in reference to the real object, when once obtained; is constant for the same objective. It becomes apparent, then, that the value of the divisions seen in the eye-piece micrometer must be found with all the objectives used, and carefully tabulated.
It was Mr. Lister who first proposed to place on the stage of the microscope a divided scale of a certain value. Viewing the scale as a microscopic object, he observed how many of the divisions on the scale attached to the eye-piece corresponded with one or more of a magnified image. If, for instance, ten of those in the eye-piece correspond with one of those in the image, and if the divisions are known to be equal, then the image is ten times larger than the object, and the dimensions of the object ten times less than that indicated by the micrometer. If the divisions on the micrometer and on the magnified scale are not equal, it becomes a mere rule-of-three sum; but in general this trouble is taken by the maker of the instrument, who furnishes a table showing the value of each division of the micrometer for every object-glass with which it will be employed.
Fig. 102.—Blood Corpuscles and Micrometer, magnified 1·3500.
Mr. Jackson’s simple and cheap micrometer is represented in [Fig. 103]. It consists of a slip of glass placed in the focus of the eye-glass, with the divisions sufficiently fine to have the value of the ten-thousandth part of an inch with the quarter-inch object-glass, and the twenty-thousandth with the eighth; at the same time the half, or even the quarter of a division may be estimated, thus affording the means of attaining considerable accuracy, and may be used to supersede the more complicated and expensive screw-micrometer, being handier to use, and not liable to derangement in inexperienced hands.
The positive eye-piece affords the best view of the micrometer, the negative of the object. The former is quite free from distortion, even to the edges of the field; but the object is slightly coloured. The latter is free from colour, and is slightly distorted at the edges. In the centre of the field, however, to the extent of half its diameter, there is no perceptible distortion, and the clearness of the definition gives a precision to the measurement which is very satisfactory.
Fig. 103.—Jackson’s Eye-piece Micrometer.
Short bold lines are ruled on a piece of glass, a, [Fig. 103], to facilitate counting, the fifth is drawn longer, and the tenth still longer, as in the common rule. Very fine levigated plumbago is rubbed into the lines to render them visible; they are then covered with a piece of thin glass, cemented by Canada balsam, to prevent the plumbago from being wiped out. The slip of glass thus prepared is secured in a thin brass frame, so that it may slide freely into its place.
Slips are cut in the negative eye-piece on each side, so that the brass frame may be pressed across the field in the focus of the eye-glass, as at m; the cell of which should have a longer screw than usual, to admit of adjustment for different eyes. The brass frame is retained in its place by a spring within the tube of the eye-piece; and in using it the object is brought to the centre of the field by the stage movements; the coincidence between one side of it and one of the long lines is made with great accuracy by means of the small screw acting upon the slip of glass. The divisions are then read off as easily as the inches and tenths on a common rule. The operation, indeed, is nothing more than the laying of a rule across the body to be measured; and it matters not whether the object be transparent or opaque, mounted or unmounted, if its edges can be distinctly seen, its diameter can be taken.
Previously, however, to using the micrometer, the value of its divisions should be ascertained with each object-glass; the method of doing this is as follows:—
Place a slip of ruled glass on the stage; and having turned the eye-piece so that the lines on the two glasses are parallel, read off the number of divisions in the eye-piece which cover one on the stage. Repeat this process with different portions of the stage-micrometer, and if there be a difference, take the mean. Suppose the hundredth of an inch on the stage requires eighteen divisions in the eye-piece to cover it; it is plain that an inch would require eighteen hundred, and an object which occupied nine of these divisions would measure the two-hundredth of an inch. Take the instance supposed, and let the microscope be furnished with a draw-tube, marked on the side with inches and tenths. By drawing this out a short distance, the image of the stage micrometer will be expanded until one division is covered by twenty in the eye-piece. These will then have the value of two-thousandths of an inch, and the object which before measured nine will then measure ten; which, divided by 2,000, gives the decimal fraction ·005.
Enter in a table the length to which the tube is drawn out, and the number of divisions on the eye-piece micrometer equivalent to an inch on the stage; and any measurements afterwards taken with the same micrometer and object-glass may, by a short process of mental arithmetic, be reduced to the decimal parts of an inch, if not actually observed in them.
In ascertaining the value of the micrometer with a deep objective, if the hundredth of an inch on the stage occupies too much of the field, then the two-hundredth or five-hundredth should be used and the number of the divisions corresponding to that quantity be multiplied by two hundred or five hundred, as the case may be.
The micrometer should not be fitted into too deep an eye-piece, as it is essential to preserve good definition. A middle-power Kellner or Huyghenian is frequently employed; at all events, use the eye-piece of lower power rather than impair the image.
The eye-lens above the micrometer should not be of shorter focus than three-quarters of an inch, even with high-power objectives.
The Ramsden Eye-piece.—The cobweb micrometer is the most efficient piece of apparatus yet brought into use for measuring the magnified image. It is made by stretching across the field of the eye-piece two extremely fine parallel wires or cobwebs, one or both of which can be separated by the action of a micrometer screw, the trap head of which is divided into a hundred or more equal parts, which successively pass by an index as the milled head is turned, shown in [Fig. 104]. A portion of the field of view is cut off at right angles to the filaments by a scale formed of a thin plate of brass having notches at its edges, the distances between which correspond to the threads of the screw, every fifth notch (as in the previous case) being made deeper than the rest, to make the work of enumeration easier. The number of entire divisions on the scale shows then how many complete turns of the screw have been made in the separation of the wires, while the number of index points on the milled head shows the value to the fraction of a turn, that may have been made in addition. A screw with one hundred threads to the inch is that usually employed; this gives to each division in the scale in the eye-piece the value of 1⁄100th of an inch. The edge of the milled head is also divided into the same number of parts.
Micrometer scale to drop into Eye-piece.
Fig. 104.—Ramsden Screw Micrometer Eye-piece.
In Watson’s Ramsden screw micrometer, [Fig. 104], the micrometer scale (seen detached) is ruled on a circular piece of glass, and this, by unscrewing the top, is dropped into its place, and one of the wires, both being fixed, is set a little to the side of the field, the teeth of the screw being cut to 1⁄100ths, and the drum giving the fractional space between the teeth to 1⁄100ths, so that the 1⁄10000th of an inch can be read off. This micrometer eye-piece is constructed entirely of aluminium, a decided advantage, being so much lighter than brass to handle.
In the screw micrometer of other makers, other modifications are found. An iris diaphragm being placed below the web to suit the power of the eye-piece employed, a guiding line at right angles to the web is sometimes added. Care should be taken to see that when the movable web coincides exactly with the fixed web, the indicator on the graduated head stands at zero.
The Compensating Eye-piece.—The very important improvements effected in the construction of the objective naturally led up to an equally useful change for the better in the eye-piece.
All objectives of wide aperture, from the curvature of their hemispherical front lenses, show a certain amount of colour defect in the extra-axial portion of the field, even if perfectly achromatic in the centre. Whether an image be directly projected by the objective, or whether it be examined with an aplanatic eye-piece, colour fringes may be detected, possibly in an increasing degree towards the periphery. This residual chromatic aberration has at length been very nearly eliminated by the aid of the compensating eye-piece.
The construction of compensating eye-pieces is somewhat remarkable, since they have an equivalent error in an opposite direction—that is, the image formed by the red rays is greater than that corresponding to the blue rays; consequently, eye-pieces so constructed serve to compensate for the unequal magnification produced by different coloured rays, and images appear free from colour up to the margin of the field.
Zeiss’s compensating eye-pieces are so arranged that the lower focal points of each series lie in the same plane when inserted in the body-tube of the microscope; no alteration of focus is therefore required on changing one eye-piece for another. This of itself is not only an advantage but also a saving of time, while the distance between the upper focal point of the objective and the lower one of the eye-piece, which is the determining element of magnification, remains constant.
Fig. 105.—A sectional view of Zeiss’s Compensating series of Eye-pieces, ½ the full size.
A.—Plane of the upper edge of the tube.
B.—Lower focal plane of eye-pieces, with their lenses in situ.
The ordinary working eye-pieces, Huyghenian and others, commencing with a magnification of four diameters, are so constructed that they can be conveniently used, as we are accustomed to use them in England, with high powers, Zeiss’s Nos. 12 and 18 compensating eye-pieces being adapted for use with his lower power apochromatic lenses of 16 and 8 mm. The numbering of the eye-pieces is carried out on the plan originally proposed by Professor Abbe—that is, the number denotes how many times an eye-piece, when employed with a given tube-length, increases the initial magnifying power of the objective, and at the same time furnishes figures for their rational enumeration. It is on this basis that the German compensating eye-pieces have been arranged in series, and in agreement with their magnifying power and distinctive numberings of 2, 4, 6, 8, 12, 18. Of these several eye-pieces, 12 is found to be the most useful. The magnification obtained by combining a compensating eye-piece with any apochromatic objective is found by multiplying its number by the initial magnification of the objective, as given in the following proof:—An objective of 3·0 mm. focus, for example, gives in itself a magnification of 83·3 (calculated, for the conventional distance of vision, 250 mm.); eye-piece 12 therefore gives with this objective a magnification of 12 × 83·3 = 1000 diameters. The classification, however, of these eye-pieces, as furnished by Abbe, is dependent upon increase in the total magnifying power of the microscope obtained by means of the eye-piece as compared with that given by the objective alone. The numbering, then, denotes how many times an eye-piece increases the magnifying power of the objective when used with a given body-tube; the proper measure of the eye-piece magnification; and, at the same time, the figures for rational enumeration.
Fig. 106.—B and C Achromatic Eye-pieces.
Compensating eye-pieces have been introduced for the correction of certain errors in high-power objectives—those made with hemispherical fronts. All such lenses, whether apochromatic or not, are greatly improved by the compensating eye-piece, but the dry objective and the lower powers are certainly deteriorated. The lower power compensating eye-pieces are Huyghenian, the higher are combinations, with no field-lens, and therefore in working act as a single or positive eye-piece. This is of importance to those who work with low powers—the older forms of objectives.
Messrs. Watson and Swift have adopted a new formula for their series of achromatic eye-pieces, whereby their magnification and flatness of field are improved. These also bear a constant ratio to the initial power of their objectives.
The compensating eye-pieces of these makers are constructed on the same principle as those of Zeiss’s for the correction of errors of colour in the marginal portion of the field, and consequently are in every way as effective as those of Continental manufacture. Figs. 106, 107, and 108 show in dotted outline the form and position of the several lenses combined in these eye-pieces.
Projection Eye-pieces are chiefly used in micro-photography, and for screen demonstrations. The cap of this eye-piece is provided with a spiral adjustment for focussing, the diaphragm being placed in front of the eye-lens, an essential arrangement for obtaining an accurate focus. The ring seen below the cap, [Fig. 108], is graduated so that the rotation for distance of screen may be carefully recorded.
Fig. 107.—The Compensating Eye-piece.
Fig. 108.—Projection Eye-piece.
Schmidt’s goniometer positive eye-piece, for measuring the angles of crystals, is so arranged as to be easily rotated within a large and accurately graduated circle. In the focus of the eye-piece a single cobweb is drawn across, and to the upper part is attached a vernier. The crystals being placed in the field of the microscope, care being taken that they lie perfectly flat, the vernier is brought to zero, and then the whole apparatus turned until the line is parallel with one face of the crystal; the frame-work bearing the cobweb, with the vernier, is now rotated until the cobweb becomes parallel with the next face of the crystal, and the number of degrees which it has traversed may then be accurately read off.
Goniometer.—If a higher degree of precision is required, then, the double-refracting goniometer invented by the late Dr. Leeson must be substituted. With this goniometer ([Fig. 109]) the angles of crystals, whether microscopic or otherwise, can be measured. It has removed the earlier difficulties incident to similar instruments formerly in use. Among other advantages, it is capable of measuring opaque and even imperfect crystals, beside microscopic crystals and those in the interior of other transparent media. It is equally applicable to the largest crystals, and will measure angles without removing the crystal from a specimen, provided only the whole is placed on a suitable adjusting stage. The value of the goniometer depends on the application of a doubly refracting prism, either of Iceland spar or of quartz, cut of such a thickness as will partially separate the two images of the angle it is proposed to measure.
Dr. Leeson strongly insisted on the importance of the microscope in the examination of the planes of crystals subjected to measurement, as obliquity in many cases arises from not only conchoidal fractures, but also from imperfect laminæ elevating one portion of a plane, and yet allowing a very tolerable reflection when measured by the double refracting goniometer.
Fig. 109.—Leeson’s Goniometer.
Microscopes for crystallographic and petrological research are now specially constructed for measuring the angles of crystals.
Erector eye-pieces and erecting prisms are employed for the purpose of causing the image presented to the eye to correspond with that of the object. They are also helpful in making minute dissections of structure; the loss of light, however, by sending it through two additional surfaces is a drawback, and impairs the sharpness of the image. Nachet designed an extremely ingenious arrangement whereby the inverted image became erect; he adapted a simple rectangular prism to the eye-piece. The obliquity which a prism gives to the visual rays when the microscope is used in the erect position, as for dissecting, is an advantage, as it brings the image to the eye at an angle very nearly corresponding to that of the inclined position in which the microscope is ordinarily used.