Page:Elementary Text-book of Physics (Anthony, 1897).djvu/438

424 is much more distinct than the other parts. How small this most sensitive area is, can be judged by carefully analyzing the effort to see distinctly the minute details of an object. For instance, in looking at the dot of an i, a change can be detected in the effort of the muscles that control the eyeball, when the attention is directed from the upper to the lower edge of the dot. The eye can then be directed with great precision to a very small object. The line joining the centre of the crystalline lens with the centre of the sensitive spot may be called the optic axis; and when the attention is directed to any particular point of an object, the eyeballs are turned by a muscular effort, until both the optic axes produced outward meet at the point. For objects at a moderate distance we have learned to associate a particular muscular effort with a particular distance, and our judgment of such distances depends mainly on this association. The angle between the optic axes when they meet at a point is called the optic angle. Our estimate of the size of an object is based on our judgment of its distance, together with the angle which the object subtends at the eye, called the visual angle. In Fig. 114, when $$ab$$ is an object and $$l$$ the crystalline lens, $$\alpha$$ is the visual angle. It is plain that the size of the image on the retina is proportional to the visual angle.

It is plain, too, that an object of twice the size, at twice the distance, would subtend the same visual angle and have an image of the same size as $$ab.$$ Nevertheless, if we estimate its distance correctly we shall estimate its size as twice that of $$ab;$$ but if in any way we are deceived as to its distance, and judge it to be less than it really is, we underestimate its size. The visual angle is the apparent size of the object.

A less precise estimate of distance can be made with a single