Compound Microscope

Now if the extreme ray OD makes an angle u with the axis of the lens, the two point sources 0 and 0' (fig. 13.c) will give rise to diffraction disks which will be just completely separated if where X represents the wave-length of the light emitted by the sources 0 and 0', and s represents the distance between 0 and 0'. The edges of the diffraction disks are, however, only very faint, consequently the images can be plainly distinguished even if the diffraction disks overlap to a quite appreciable extent. The distribution of brightness indicated in fig. 13.d, corresponds to the relation Between the two brightest points there is, in this case, a line in which the intensity is 97% of that at the two maxima. This is probably sufficient for the two maxima to be just distinguishable. For a trained observer with eyes of normal acuity, the limit of resolution obtainable may thus be taken as about If the medium has a refractive index n, the wave-length of the light will be shorter than it would be in air, in the proportion i/n. We can use the wave-length as measured in air, in this formula by substituting for X, when we obtain The quantity nsinu is a property of the lens, since it depends on u and on the refractive index of the medium in which the lens is intended to be used on the object side; it is called the numerical aperture of the lens. For a "dry-front" lens n is unity, and the maximum numerical aperture such a lens can have is 1.

Immersion Lenses.

Many lenses are designed for use with a layer of fluid filling the space between the front of the lens and the object or cover-glass. The maximum numerical aperture such an immersion lens can have is determined by the refractive index of the immersion fluid, by the refractive index of the cover glass (if any) over the object, or by the refractive index of the front lens of the object-glass, whichever of these three has the lowest value. The front lens of an immersion object-glass is usually made of crown glass of refractive index 1.508 to 1.525; the cover-glasses most commonly used have a refractive index between 1.515 and 1.525. For most immersion lenses, therefore, a thickened cedar-wood oil, having a refractive index of 1.515 to 1.525, is used as the immersion fluid. For obtaining still higher resolving powers, object-glasses have been made with front lenses of refrac tive indices up to 1.66, for use with proper immersion fluids. A homogeneous immersion lens is an object-glass designed for use with an immersion fluid having the same refractive index as its front lens.

Aberrations of Object-glasses.

Unless the aberrations of the lens are very small, the actual resolving power will fall short of that corresponding to the numerical aperture, except with certain special methods of illumination which may give a sem blance of resolution. In an object-glass, therefore, we require, in addition to a reasonable magnifying power, (a) an appropriately large numerical aperture and (b) the most nearly perfect cor rections it is possible to obtain over the whole of this aperture.

Spherical aberration can be corrected by combining together individual lenses, of suitable forms, all made of one kind of glass. A more usual method is to use combinations of lenses of different glasses which may either be cemented or may be mounted at suitable distances from each other and separated by air. This method lends itself to the simultaneous correction of both spherical and chromatic aberra tions, and is therefore used for all ordinary microscope object glasses. In the more powerful object-glasses several individual lenses and lens systems must be used in order to obtain the requisite degree of correction over the whole aperture (fig. To secure a good image of a small object it is not sufficient merely to correct the spherical aberration for a point on the axis of the object-glass. It is necessary, in addition, that the light in the object plane be brought to focus in the corresponding area in the image plane. Seidel (1856) and Clausius (1864) investigated the conditions which must be fulfilled to obtain this, and showed that there must be a definite relation between the inclinations of the rays on the object side and the inclinations of the corresponding rays on the image side. Helmholtz and Abbe investigated this independently in 1873 with similar results. The condition is, if a ray from a point lying on the axis in the object plane is inclined to the axis at an angle u, the corresponding ray on the image side must be inclined to the axis at an angle u' such that where C has the same value for every ray coming from the point in question. Abbe drew special attention to the importance of this condition being satisfied in designing microscope object glasses, and gave to it the name of the "sine-condition." If the axial spherical aberration has been corrected but the sine-con dition has not been fulfilled, the pencils of rays which come from a point a little off the axis are brought to focus at different distances from the axis on the image side (fig. 5), giving different magnifications according to the zone of the lens through which the pencils pass.

Chromatic aberrations can be corrected by using lens combina tions in which the individual lenses are made of different types of glass.. A negative lens of low power, made of flint glass, will produce a dispersion equal and opposite to that produced by a positive lens of considerably higher power made of crown glass. Two such lenses, correctly combined together, will act as a positive lens with a common focus for both the blue and red rays. Such a lens is called an achromatic lens.