Fig. 35.--Relative diameters of the (utilized) back lenses of various dry and immersion objectives of the same power (1/4-in.) from an air angle of 60° to an oil angle of 180°.] Thus we arrive at a general proposition for all kinds of objectives: 1st, when the power is the same, the admission of rays (or aperture) varies with the diameter of the pencil at its emergence; 2nd, when the powers are different, the same aperture requires different openings in the ratio of the focal lengths, or conversely with the same opening the aperture is in inverse ratio to the focal lengths. We see, therefore, that just as in the telescope the absolute diameter of the object-glass defines its _aperture_, so in the microscope _the ratio between the utilised diameter of the back lens and the focal length_ of the objective defines its aperture also, and this is clearly a definition of aperture in its primary and only legitimate meaning as “opening;” that is, the capacity of the objective for admitting rays from the object and transmitting them to the image. If, by way of illustration, we compare a series of dry and oil-immersion objectives, and commencing with small air angles, progress up to 180° air angle, and then take an oil-immersion of 82° and progress again to 180° oil angle, the ratio of opening to power progresses also, and attains its maximum, not in the case of the air angle of 180° (when it is exactly equivalent to the oil angle of only 82°), but is greatest at the oil angle of 180°. If we assume the objectives to have the same power throughout we get rid of one of the factors of the ratio, and we have only to compare the diameters of the emergent beams, and can represent their relations by diagrams. Fig. 35 illustrates five cases of different apertures of 1/4-in. objectives, viz.: those of dry objectives of 60°, 97°, and 180° air angle, a water-immersion of 180° water angle, and an oil-immersion of 180° oil angle. The inner dotted circles in the two latter cases are of the same size as that corresponding to the 180° air angle. A dry objective of the maximum air angle of 180° is only able to utilise a diameter of back lens equal to twice the focal length, while an immersion lens of even only 100° utilises a _larger_ diameter, _i.e._, it is able to transmit more rays from the object to the image than any dry objective is capable of transmitting. Whenever the angle of an immersion lens exceeds twice the critical angle for the immersion fluid, _i.e._, 96° for water or 82° for oil, its aperture is in excess of that of a dry objective of 180°. [Illustration: Fig. 36.]