Concave specula have properties very different from those which are convex; they are of more importance in the construction of reflecting telescopes and other optical instruments; and therefore require more minute description and illustration. Concave mirrors cause parallel rays to converge; they increase the convergence of rays that are already converging; they diminish the divergence of diverging rays; and, in some cases, render them parallel and even convergent; which effects are all in proportion to the concavity of the mirror. The following figures show the course of diverging and parallel rays as reflected from concave mirrors. Fig. 20 represents the course of _parallel_ rays, and AB, the concave mirror on which they fall. In this case, they are reflected so as to unite at F, which point is distant from its surface _one fourth_ of the diameter of the sphere of the mirror. This point is called the focus of parallel rays, or _the true focus of the mirror_. And, since the sun beams are parallel among themselves, if they are received on a concave mirror, they will all be reflected to that point, and there burn in proportion to the quantity of rays collected by the mirror. Fig. 21. shows the direction of _diverging_ rays, or those which proceed from a near object. These rays proceeding from an object further from the mirror than the true focal point, as from D to A and to B, are reflected converging and meet at a point F, _further from the mirror_ than the focal point of parallel rays. If the distance of the radiant, or object D, be equal to the radius CE, then will the focal distance be likewise equal to the radius: That is, if an object be placed in the center of a concave speculum, the image will be reflected upon the object, or they will seem to meet and embrace each other in the centre. If the distance of the radiant be equal to half the radius, its image will be reflected to an infinite distance, for the rays will then be parallel. If, therefore, a luminous body be placed at half the radius from a concave speculum, it will enlighten places directly before it at great distances. Hence their use when placed behind a candle in a common lantern; hence their utility in throwing light upon objects in the Magic Lantern and Phantasmagoria, and hence the vast importance of very large mirrors of this description, as now used in most of our Light Houses, for throwing a brilliant light to great distances at sea to guide the mariner when directing his course under the cloud of night. [Illustration: _figure 20._] [Illustration: _figure 21._] When _converging_ rays fall upon a concave mirror, they are reflected more converging and unite at a point between the focus of parallel rays and the mirror; that is, nearer the mirror than one half the radius; and their precise degree of convergency will be greater than that wherein they converged before reflection. _Of the images formed by Concave Mirrors._