Page:Elementary Text-book of Physics (Anthony, 1897).djvu/440

436 $$Oa,$$ when the angle subtended is $$aOb.$$ The ratio of these angles is very nearly that of $$Oa$$ to $$OF.$$ Hence the magnifying power is the ratio of the distance of distinct vision to the focal length of the lens.

348. The Compound Microscope.—A still greater magnifying power may be obtained by first forming a real enlarged image of the object (§ 339) and using the magnifying-glass upon the image, as shown in Fig. 116. The lens $$A$$ is called the objective, and $$E$$ is called the eye-lens or ocular. As will be seen in § 359, both $$A$$ and $$E$$ often consist of combinations of lenses for the purpose of correcting aberration.

349. Telescopes.—If a lens or mirror be arranged to produce a real image of a distant object, either on a screen or in the air, we may observe the image at the distance of distinct vision, when the visual angle for the object is enlarged in the ratio of the focal length of the lens to the distance of distinct vision. This will be plain from Fig. 117. Suppose the nearest point from which the object can be observed by the naked eye to be the centre of the lens $$O.$$

The visual angle is then $$AOB = aOb,$$ while the visual angle for the image is $$aEb.$$ Since these angles are always very small, we have $$\frac{aEb}{aOb} = \frac{Oc}{Ec}$$ very nearly. But when $$AB$$ is at a great distance, $$Oc$$ is the focal length of the lens. By using a magnifying-glass to observe the image, the magnifying power may be still further increased in the ratio of the distance of distinct vision to the focal length of the magnifying-glass. The magnifying power of the combination is therefore the ratio of the focal length of the object-glass to the focal length of the eye-glass. A concave mirror may be substituted for the object-glass for producing the real image.