All points lying out of this plane are reproduced as circles of confusion. 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 undertakes 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). |
 |
 |
|
| Fig. 5. | Fig. 6. | Fig. 7. |
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 individual components 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 plano-convex lenses, the focal lengths of which are in the ratio of 3 : 1; the plane
| Wollaston. | Fraunhofer. | Wilson. | Steinheil. | Chevalier (Brücke). |
 |
 |
 |
 |
|
| Fig. 8. | Fig. 9. | Fig. 10. | Fig. 11. | Fig. 12. |
sides are turned towards the object, and the smaller of the two lenses is nearer the object. This construction was further improved (1) 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 110 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. 10). 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 × 40, are chromatically and spherically corrected, and for a middle diaphragm the errors of lateral pencils, distortion, astigmatism and coma are eliminated. “Peephole” 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 proposed by Chevalier and carried out by E. Brücke 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 microscopes 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