348. =Visual Angle.=--In order that you may understand the operation of lenses in relation to vision I must first explain to you what is meant by the visual angle. In Fig. 236 (p. 270) are represented arrows of the same size at different distances from the eye. From the ends of each of the arrows are drawn lines to the eye. The angle which these lines make in each case as they meet at the eye is termed the visual angle. Now the apparent size of an object depends upon the size of this angle. The degrees of the angles are marked upon the figure. Thus the visual angle of the nearest arrow is 120 degrees, and that of the second is 60, only half as large. The first arrow therefore appears twice as large as the second. For the same reason it appears four times as large as the third, eight times as large as the fourth, and twelve times as large as the fifth. The same thing is illustrated in another way in Fig. 237. Here the arrows _e f_, _g h_, and _i k_ appear to the eye as large as A B, because they have the same visual angle, and for this reason make an image of the same size in the eye, as you see is indicated in the figure. It is hardly necessary to say that what is true of objects as a whole is true also of any part of them. Each part, however small, has its visual angle, and this governs its apparent size. [Illustration: Fig. 238.] [Illustration: Fig. 239.] 349. =Lenses.=--Transparent bodies having curved surfaces are called lenses. There are six kinds, represented in Fig. 238. The lenses in most common use are the double convex and double concave. The explanation of the mode in which these act upon light will sufficiently illustrate the operation of the others. They act by refraction, the convex collecting the rays, or bringing them nearer together, and the concave putting them farther apart. You can at once see, then, that a convex lens by causing the rays coming from an object to converge more, increases the visual angle, and therefore makes the object to appear larger than it otherwise would. This effect is illustrated by Fig. 239. The rays of light coming from the arrow are made by the lens so to converge as to meet at _a_, instead of _b_, where they would meet if they did not pass through the lens. That is, by passing through the lens they have a larger visual angle, and therefore the object is magnified. The distance between, _c_ and _d_ shows the size which the arrow would appear to have to the eye placed at _a_. [Illustration: Fig. 240.]