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Originally appearing in Volume V18, Page 395 of the 1911 Encyclopedia Britannica.
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SIMPLE MICROSCOPE Position and Size of the Image.—A person with normal vision can see objects distinctly at a distance varying from ten. inches to a very great distance. Objects at different distances, however, are not seen distinctly simultaneously, but in succession. This is effected by the power of accommodation of the eye, which can so alter the focal length of its crystalline lens that images of objects at different distances can be produced rapidly and distinctly one after another upon the retina. The angle under which the object appears depends upon the distance and size of the object, or, in other words, the size of the image on the retina is determined by the distance and the dimensions of the object. The ratio between the real size of the object y (fig. 1) 1 and the distance 1, which is equal to the tangent of the visual angle w, is termed the " apparent size " of the object. From the figure, which represents vision with a motionless eye, it is seen that the apparent size increases as the object under observation is approached. The greater the visual angle, the more distinctly are the details of the object perceived. On the other hand, as the observer recedes from the object, the apparent size, and also the image on the retina diminishes; details become more and more confused, and gradually, after a while, disappear altogether, and ultimately the external configuration of the object as a whole is no longer recognizable. This case arises when the visual angle, under which the object appears, is approximatel}, a minute of arc; it is due to the physiological construction of the retina, for the ends of nerve fibres, which receive the impression of light, have themselves a definite size. The lower limit of the resolving power of the eye is reached when the distance is approximately 3438 times the size of the object. If the object be represented by two separate points, these points would appear distinct to the normal eye only so long as the distance between them is at the most only 3438 times smaller than their distance from the eye. When the latter distance is increased still further, the two appear as one. Therefore when it is desired to distinctly recognize exceedingly small objects or details of such, they are brought as near as possible to the eye. The eye is strained in bringing its focal length to the smallest possible amount, and when this strain is long continued it may cause pain. When the shortest distance obtained by the highest strain of accommodation is insufficient to recognize small objects, distinct vision is possible at even a shorter distance by placing a very small diaphragm between the eye and the object, the pencils of rays proceeding from the object-points, which otherwise are limited by the pupils of the eye, being thus restricted by the. diaphragm. The object is then projected with such acute pencils on the plane focused for, in this case on the plane on which the eye can just accommodate itself, that the circle of confusion arising there is still so small that it is below the limit of angular visual distinctness and on that account appears as a sharp point. However, the loss of light in this procedure is extraordinarily large, so that only most intensely illuminated objects can be investigated. A naked short-sighted eye, which would be corrected for distant objects by a spectacle glass of —Io diopters, may approach the object up to about 4 in. and have a sharp image upon the retina without any strain whatever. For the observation of small objects, a myopic eye is consequently superior to a normal eye; and the normal eye in its turn is superior to the hypermetropic one. When the details are no longer recognizable by the unaided eye, the magnifying glass or the simple microscope is necessary. As a rule large magnification is not demanded from the former, but a larger field of view, whilst the simple microscope should ensure powerful magnification even when the field is small. The simple microscope enlarges the angle of vision, and does not tire the eye when it is arranged so that the image lies in the farthest limit of distinct vision (the punctum remotum). A normal eye will therefore see an image formed by the magnifying glass most conveniently when it is produced at a great distance, i.e. when the object is in its front focal plane. If y (fig. 2) be the object the image appears to a normal L Regulation of the Rays?--In using optical instruments the eye in general is moved just as in free vision; that is to say, the attention is fixed upon the individual parts of the image one after another, the eye being turned in its cavity. In this case the eye is always directed so that the part of the image which is wished to be viewed exactly falls upon the most sensitive portion of the retina, viz. the macula lutea (yellow spot). Corresponding to the size of the yellow spot only a small fraction of the image appears particularly distinctly. The other portions which are reproduced on the retina on the regions surrounding the yellow spot will also be perceived, but with reduced definition. These external and less sensitive parts of the retina, therefore, merely give information as to the general arrangement of the objects and to a certain extent act as guide-post in order to show quickly and conveniently, although not distinctly, the places in the image which should claim special attention. Vision with a motionless eye, or " indirect vision," gives a general view over the whole object with particular definition of a small central portion. Vision with a movable eye, or direct vision," gives exact information as to the parts of the object one after another. The simple microscope permits such vision. If the instrument has a sensible lens diameter, and is arranged so that the centre of rotation of the eye can coincide with the intersection of the principal rays, the lens can then form with the eye a centred system. Such lenses are termed " lenses for direct vision." By moving the eye about its centre of rotation M the whole field can be examined. The margin of the mount of the lens serves as the diaphragm of the field of view. The selection of the rays emerging from the lens and actually employed in forming the image is undertaken by the pupil of the eye which, in this case, is consequently the exit pupil of the instrument. In fig. 3 P'P'1 designates the exit pupil of the L eye situated behind the system L with passive accommodation at a very great distance under the angle w'. Since H' P = F 0, = y, from the focal length of the simple microscope, the visual angle w' is given by tan w'/y=I/f'=V, (I) in which f', = H' F', is the image-side focal length (see LENS). Since the lens is bounded by air, the image- and object-side focal lengths f' and f are equal. The value 1/f' or V in (1), is termed the power of the lens. In most cases the number of " diameters " of the simple microscope is required; i.e. the ratio between the apparent sizes of the object when observed through the microscope and when viewed by the naked eye. When a person of normal vision views a small object, he brings it to the distance of distinct vision, which would average about lo in. The apparent size is then (fig. I) tan w = y/l, where l = lo in., whilst the apparent size of the object viewed through the magnifying glass would result from the formula (I) tan w' =y/f. Consequently the number of diameters will be N = tan w'/tan w = y/f . l/y = l/f =V.1; (2) it is thus equal to the magnifying power multiplied by the distance of distinct vision, or the number of times that the focal length is contained in io in. Since this value for the distance of distinct vision is only conventional, it is understood that the capacity of the simple micro-scope given in (2) holds good only for eyes accustomed to examine small objects to in. away; and observation through the magnifying glass must be undertaken by the normal eye with passive accommodation. A lens of I in. focal length must be spoken of, according to this notation, as a X to lens, and a lens of is in. focal length as a X too lens. Obviously the position of a normal eye free from accommodation is immaterial for determining the magnification. A X to magnification is, however, by no means guaranteed to a myopic eye of—to D by a lens of i in. focus. Since this short-sighted observer can view the object with the naked eye with no inconvenience to himself at 4 in. distance, it follows (to him) the apparent size is tan w =y/4; and to secure convenient vision through the lens the short-sighted person would bring the object to such a distance that a virtual, magnified image would be projected in his punctum remotum. In addition it will be supposed that the centre of the pupil of the observer coincides with the back focal point of the system. The apparent size of the object seen through the lens is then tan w' = y/f. The magnification, resulting from the simple microscope of 1 in. focus, is here N=tan w'/tan w= y/f•4/y=4/f=4. Thus, while a lens of I in. focal length assures to the normal-sighted person a X to magnification, it affords to the short-sighted individual only X 4. On the other hand, it is even of greater use to the hypermetropic than to the observer of normal sight. From this it appears that each observer obtains specific advantages from one and the same simple microscope, and also the individual observer can obtain different magnifications by either using different accommodations, or by viewing in passive accommodation. vFIG. 3. lens, and the image of P'P'1, i.e. PP1, which is formed by the lens, limits the aperture of the pencils of rays on the object-side; consequently it is the entrance pupil of the instrument. Since the exit pupil moves in observing the whole field, the entrance pupil also moves. The principal rays, which on the object-side connect the object-points with the centre of the entrance pupil, intersect the axis on the image-side at the centre of rotation M of the eye. M is therefore the intersection of the principal rays. So long as the exit pupil is completely filled the brightness of the image will be approximately equal to that of free vision. If, however, we fix the points lying towards the margin of the field of view, the diaphragm gradually cuts off more and more of the rays which were necessary to fill the pupil, and in consequence the brightness gradually fall's off to zero. This vignetting can be observed in all lenses. In most cases, and also in corrected systems, the intersection of the principal rays is no longer available for the centre of rotation of the eye, and this kind of observation is impossible. In some instruments observation of the whole available field is only possible when the head and eye are moved at the same time, the lens retaining its position. Dr M. von Rohr terms this kind of vision " peep .hole observation." It has mainly to be considered in connexion with powerful magnifying glasses. In most cases a diaphragm regulates the rays. Fig. 4 shows the position of the diaphragms to be considered in this kind of observation. PP1 is the" entrance pupil, P'P1' the exit pupil, and GG the diaphragm. The inter-section of the principal rays in this case lies in the middle of the entrance pupil or of the exit pupil. By head and eye motion FIG. 4. the various parts of the whole field can be viewed one after another. The distance of the eye from the lens is here immaterial. In this case also the illumination must fall to zero by the vignetting of the pencils coming from objects at the margin of the field of view. C and D are the outermost rays which can pass through the instrument. Magnifying glasses are often used for viewing three-dimensional objects. Only points lying on the plane focused for can be sharply reproduced in the retina, which acts as object-plane to the retina. 1 See also LENS. All points lying out of this plane are reproduced as circles of con-fusion. The central projection, of which the centre is the middle point of the entrance pupil on the plane focused for, will show in weaker systems, or those very much stopped down, a certain finite depth of definition; that is to say, the totality of points, which lie out of the plane focused for, and which are projected with circles of confusion so small that they appear to the eye as sharp points, will include the sharp object relief, and determine the depth of definition of the lens. With increasing magnification the depth of definition diminishes, because the circles of confusion are greater in consequence of the shorter focal length. Very powerful simple microscopes have hardly any depth of definition so that in fact only points lying in one plane can be seen sharply with one focusing. Illumination.—So long as the pupil of the observer alone under-takes the regulation of the rays there is no perceptible diminution of illumination in comparison with the naked eye vision. The losses of light which occur in this case are due to reflection, which takes place in the passage of the light through the glass surfaces. In a lens with two bounding surfaces in air there is a loss of about 9 %; and in a lens system consisting of two separated lenses, i.e. with four surfaces in air, about 17 %. Losses due to absorption are almost zero when the lenses are very thin, as with lenses of small diameter. A.very marked diminution in illumination occurs, however, when the exit pupil of the instrument is smaller than the pupil of the eye. In such instruments an arrangement is often required to intensely illuminate the object. Forms of the Simple Microscope.—If the ordinary convex lens be employed as magnifying glass, great aberrations occur even in medium magnifications. These are: (1) chromatic aberration, (2) spherical aberration and (3) astigmatism (see ABERRATION). When the pupil regulates the aperture of the rays producing the image the aberrations of the ordinary lenses increase considerably with the magnification, or, what 'amounts to the same thing, with the increase in the curvature of the surfaces. For lenses of short focus the diameter of the pupil is too large, and diaphragms must be employed which strongly diminish the aperture of the pencils, and so reduce the errors, but with a falling off of illumination. To reduce the aberrations Sir David Brewster proposed to employ in the place of glass transparent minerals of high refractive index and low dispersion. In this manner lenses of short focus can be produced having lower curvatures than glass lenses necessitate. The diamond has the requisite optical properties, its index of refraction being about 1.6 times as large as that of ordinary glass. The spherical aberration of a diamond lens can be brought down to one-ninth of a glass lens of equal focus. Apart, however, from the cost of the mineral and its very difficult working, a source of error lies in its want of homogeneity, which often causes a double or even a triple image. Similar attempts made by Pritchard with sapphires were more successful. With this mineral also spherical and chromatic aberration are a fraction of that of a glass lens, but double refraction, which involves a doubling of the image, is fatal to its use. Improvements in glass lenses, however, have rendered further experiments with precious stones unnecessary. The simplest was a sphere of glass, the equator of which (i.e. the mount) formed the diaphragm. Wollaston altered this by taking two plano-convex lenses, placing the plane surfaces towards each other and employing a diaphragm between the two parts (fig 5). Wollaston. Brewster. Brewster (Stanhope). Sir David Brewster found that Wollaston's form worked best when the two lenses were hemispheres and the central space was filled up with a transparent cement having the same refractive index as the glass; he therefore used a sphere and provided it with a groove at the equator (see fig. 6). Coddington employed the same construction, and for this reason this device is frequently called the Coddington lens; although he brought the Wollaston-Brewster lens into general notice, he was neither the inventor nor claimed to be. This lens reproduced all points of a concentric spherical surface simultaneously sharp. A construction also employing one piece of glass forms the so-called Stanhope lens (fig. 7), which was really due to Brewster. This is a glass cylinder, the two ends of which are spherical surfaces. The more strongly curved surface is placed next the eye, the other serves at the same time as specimen carrier. This lens is employed in articles found in tourist resorts as a magnifying glass for miniature photographs of the locality. Doublets, &c.—To remove the errors which the above lenses showed, particularly when very short focal lengths were in question, lens combinations were adopted. The individualcomponents required weaker curvatures and permitted of being more correctly manufactured, and, more particularly, the advantage of reduced aberrations was the predominant, factor. Wollaston's doublet (fig. 8) is a combination of two piano-convex lenses, the focal lengths of which are in the ratio of 3 : I ; the plane Wollaston. Fraunhofer. Wilson. Steinheil. Chevalier (Brucke). sides are turned towards the object, and the smaller of the two lenses is nearer the object. This construction was further improved (I) by introducing a diaphragm between the two lenses; (2) by altering the distance between the two lenses; and (3) by splitting the lower lens into two lenses. Triplets are employed when the focal length of the simple microscope was less than in. When well made such constructions are almost free from spherical aberration, and the chromatic errors are very small. Similar doublets composed of two plano-convex lenses are the Fraunhofer (fig. 9) and the Wilson (fig. 1o). Axial aberration is reduced by distributing the refraction between two lenses; and by placing the two lenses farther apart the errors of the pencils of rays proceeding from points lying outside the axis are reduced. The Wilson has a greater distance between the lenses, and also a reduction of the chromatic difference of magnification, but compared with the Fraunhofer it is at a disadvantage with regard to the size of the free working distance, i.e. the distance of the object from the lens surface nearer it. By introducing a dispersive lens of flint the magnifying glass could be corrected for both chromatic and spherical aberrations. Browning's " platyscopic " lens and the Steinheil " aplanatic " lens (fig. 11) are of this type. Both yield a field of good definition free from colour. The manner in which the eye uses such a lens was first effectively taken into account by M. von Rohr. These anastigmatic lenses, which are manufactured up to X 40, are chromatically and spherically corrected, and for a middle diaphragm the errors of lateral pencils, distortion, astigmatism and coma are eliminated. " Peep-hole ' observation is employed, observation being made by moving the head and eye while the lens is held steady. Even in powerful magnifications a good image exists in all parts of a relatively large field, and the free working distance is fairly large. For especially large free working distances the corrections pro-posed by Chevalier and carried out by E. Briicke must be noticed (fig. 12). To an achromatic collective lens, which is turned towards the object, a dispersive lens is combined (this type to a certain extent belongs to the compound microscope). By altering the distance of the collective and dispersive members the magnification can be widely varied. Through the large free working distance, which for certain work offers great advantages, the size of the field of view is diminished. In magnifying glasses for direct vision the eye must always be considered. The lens is brought as close as possible to the eye so as to view as large a field as possible. The watchmaker's glass is one of the earliest forms of this kind. Gullstrand showed how to correct these lenses for direct vision, i.e. to eliminate distortion and astigmatism when the centre of rotation of the eye coincided with the point where the principal rays crossed the axis. Von Rohr fulfilled this condition by constructing the Verant lens, which are low power systems intended for viewing a large flat field. Stands.—For dissecting or examining objects it is an advantage to have both hands free. Where very short focus simple micro-scopes are employed, using high magnifications, it is imperative to employ a stand which permits exact focusing and the use of a special illuminating apparatus. Since, however, only relatively low powers are now employed, the ordinary rack and pinion movement for focusing suffices, and for illuminating the object only a mirror below the stage is required when the object is transparent, and a condensing lens above the stage when opaque. Dissecting stands vary as to portability, the size of the stand, and the manner in which the arm-rests are arranged. A stand is shown in fig. 57 (Plate). On the heavy horseshoe foot is a column carrying the stage. In the column is the guide for the rack-and-pinion movement. Lenses of various magnifications can be adapted to the carrier and moved about over the stage. The rests can be attached to the stage, and when done with folded together. Illumination of transparent objects is effected by the universal-jointed mirror. By turning the knob A, placed at the front corner of the stage, a black or white plate, forming a dark or light back-ground, can be swung underneath the specimen. When the recognition of the arrangement in space of small objects is desired a stereoscopic lens can be used. In most cases refracting and reflecting systems are arranged so that the natural interpupillary distance is reduced. Stereoscopic lenses can never be powerful systems, for the main idea is the recognition of the depth of objects, so that only systems having a sufficient depth of definition can be utilized. Very often such stereoscopic lenses, owing to faulty construction, give a false idea of space, ignoring the errors which are due to the alteration of the inter-pupillary distance and the visual angles belonging to the principal rays at the object-side (see BINOCULAR INSTRUMENTS).
End of Article: SIMPLE
SIMPLE CHOLERA (synonyms, Cholera Europaea, British...

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