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 −10 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.
Fig. 2.
If y (fig. 2) be the object the image appears to a normal eye situated behind the system L with passive accommodation at a very great distance under the angle w ′. Since H′ P＝F O,＝y, from the focal length of the simple microscope, the visual angle w′ is given by
| tan w ′/y＝1/f ′＝V, | (1) |
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 10 in. The apparent size is then (fig. 1) tan w＝y/l, where l＝10 in., whilst the apparent size of the object viewed through the magnifying glass would result from the formula (1) tan w ′ =y/f. Consequently the number of diameters will be
| N＝tan w ′/tan w＝y/f . l/y＝l/f＝V.l; | (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 10 in.
Since this value for the distance of distinct vision is only conventional, it is understood that the capacity of the simple microscope given in (2) holds good only for eyes accustomed to examine small objects 10 in. away; and observation through the magnifying glass must be undertaken by the normal eye with passive accommodation. A lens of 1 in. focal length must be spoken of, according to this notation, as a × 10 lens, and a lens of 110 in. focal length as a × 100 lens. Obviously the position of a normal eye free from accommodation is immaterial for determining the magnification. A × 10 magnification is, however, by no means guaranteed to a myopic eye of −10 D by a lens of 1 in. focus. Since this shortsighted 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 1 in. focal length assures to the normal-sighted person a × 10 magnification, it affords to the short-sighted individual only × 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.
Regulation of the Rays.[1]—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.
Fig. 3.
In fig. 3 P′P′1 designates the exit pupil of the 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 falls off to zero. This vignetting can be observed in all lenses.
Fig. 4.
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 intersection 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 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.