The object-glasses of the microscope, consisting of the compound lenses, have their aberrations balanced to a considerable extent on the above principles—the lowest combination being under-corrected, while the upper combinations are over-corrected; and, by suitable adaptation of their distance from each other, further correction may be obtained, the aberration of the object-glass altogether being, however, over-corrected or negative.
The eye-piece consists of two simple plano-convex lenses, the upper or eye-glass (fig. 27 e) having a shorter focus than the lower (f) or field-glass, and the two placed at the distance of half the sum of their focal lengths. The object-glass alone would form an enlarged and reversed image of the object within the body of the microscope, the cones of rays from each point of the object terminating at the larger arrows in the figure (fig. 27). But the rays meeting the field-glass are brought by it to a focus at the position of the smaller arrows, where they form a reduced image; and, subsequently passing through the eye-glass, they are so altered in direction as to enter the eye at a greater angle, and to present a magnified image of the object.
The eye-piece produces several important effects. The refraction being produced by two less convex lenses instead of one of greater convexity, the spherical aberration is considerably reduced; and the convexities of the lenses in the eye-piece being situated in an opposite direction to that of those in the object-glass, the spherical aberration of the former reverses and so neutralizes that of the latter. Also the under-correction of the field-glass compensates the over-correction of the object-glass—the blue rays which are refracted more than the red by the field-glass, being thrown upon the eye-glass nearer its centre, where the refraction is less, and thus the coloured rays become parallel or nearly so on reaching the eye. Moreover the field-glass collects a larger number of rays than the eye-glass could do alone, so that it enlarges the field and increases its brightness.
In the best object-glasses the aberrations are so well balanced that the mere covering an object with thin glass is sufficient to disturb the balance and render very delicate markings either misty and coloured or wholly invisible. The effect produced by a plate of glass may be understood by reference to fig. 26, the rays being supposed to emanate from the object at a; and it is evident that the refraction of the glass so alters the direction of the rays that they will fall upon the lower combination nearer the centre than if the cover were absent, and thus negative aberration is produced. In the best object-glasses, however, this aberration may almost entirely be removed, the lower combination being susceptible of approximation by a screw movement to the second or next above it, so that the ascending rays, being able to continue their oblique course through the increased distance between the object and the lower combination, may fall upon the same portions of the latter that they did before the cover was applied.
Polarization of Light.—In attempting to give a sketch of this curious and difficult subject, we must suppose the reader to be in possession of a natural crystal of calcareous spar, and either two Nicol’s prisms (forming the ordinary polariscope) or two plates of the mineral called tourmaline cut in the direction of the length or axis of the crystal.
Hitherto we have considered rays of light falling upon transparent substances as simply refracted or reflected according to the ordinary laws of refraction or reflexion. We have now to notice some curious exceptions, forming the basis of many interesting phenomena, especially in connexion with the microscope, in which these laws are more or less deviated from. If we place a plate of tourmaline, cut as above directed, upon or beneath the stage of the microscope, the light will pass through it, appearing tinged with the green or brown colour natural to the tourmaline; but on laying another slice upon the eye-piece, and turning the latter round or rotating it, the light will be transmitted in certain positions only, being partially or entirely arrested in others, so that the field appears black. And, on careful examination, it will be noticed that the change from black to white occurs at each quarter of a rotation, being twice black and twice white in an entire rotation, the changes occurring alternately. The same phenomena may also be exhibited by substituting two Nicol’s prisms for the tourmalines.
Again, if we take a natural crystal of calcareous spar, and paste upon one side of it a piece of black paper with a small hole in the middle, on holding the crystal to the light or over a piece of white paper, with the covered side next the light, two holes or two images of the hole will be seen; and if the crystal without the paper be placed over some print, the print will appear double. Hence the light passing through the hole is twice or doubly refracted, one ray following the ordinary law of refraction, while the other follows a different law, being retarded and pursuing a longer course; and so the two rays are called respectively the ordinary and extraordinary ray. And on viewing these through a tourmaline or a Nicol’s prism, as in the experiment with the two tourmalines, the images will become alternately visible and invisible, just as was then the case with the entire mass of light.
The light which has undergone this singular change is said to be polarized, because the rays appear to have acquired poles or sides. In the above experiments the lower prism or tourmaline is called the polarizer, because it polarizes the light, and the upper is called the analyzer, because it analyzes or tests the light altered by the former.
An idea of the cause of this change may be obtained by reference to the undulatory theory of light. Ordinary light consists of waves or undulations taking place in planes at right angles to each other, or in all planes; while in polarized light the undulations are all in one plane or in parallel planes. This may perhaps be understood by considering that books in a book-case are situated in parallel planes, the shelves being in planes at right angles to the former. And by imagining in polarizing substances the existence of some structure acting like a grating, a notion can be obtained how the rays in the different planes may be transmitted or intercepted. If the grating be so placed that the bars (representing the planes of polarization) are perpendicular, the books can pass between them; while if the grating be turned round a quarter of a circle, they will become transverse, and the books cannot pass, while the shelves could do so. Carrying on this analogy, the tourmaline or Nicol’s prism polarizes the light by transmitting only those rays whose undulations are in planes parallel to the bars; while the analyzer allows these undulations to pass through it when the direction of the planes coincides with that of the bars, but interrupts them when their direction is at right angles to the bars. And it is evident that the planes of polarization of the ordinary and extraordinary rays are opposite, from the opposite action of the analyzer upon them.
The power of doubly refracting and polarizing is not possessed by all crystalline bodies, but only those belonging to other than the cubic system; crystals belonging to this system neither doubly refract nor polarize light. In all doubly refracting crystals there are one or more lines or directions in which the light is not doubly refracted. These are called the optic axes, and sometimes they coincide with the geometric axis of the crystals, at others they do not; and they may be regarded as positions or directions of equilibrium of certain molecular forces existing within the crystal, which, acting in opposition, neutralize each other.