In considering the action of a lens we can regard any lens as being built up of a number of prisms with curved faces in contact. Such a lens is shown in Fig. 67, the light rays being refracted towards the base of the prisms or towards the normal, as already explained; while the top half of the lens will refract all the light downwards, the bottom half will act as a series of inverted prisms and refract all the light upwards.
If a beam of parallel light—such as light from the sun—be passed through a double convex lens L, Fig. 68, we shall find that the rays have been refracted from their parallel course and brought together at a point F. This point F is
termed the principal focus of the lens, and its distance from the lens is known as the focal length of that lens. In a double and equally convex lens of glass the focal length is equal to the radius of the spherical surfaces of the lens. If the lens is a plano-convex the focal length is twice the radius of its spherical surfaces. If the lens is unequally convex the focal length is found by the following rule: multiply the two radii of its surfaces and divide twice that product by the sum of the two radii, and the quotient will
be the focal length required. Conversely, by placing a source of light at the point F the rays will be projected in a parallel beam the same diameter as the lens. If, however, instead of being parallel, the rays proceed from a point farther from the lens than the principal focus, as at A, Fig. 69, they are termed divergent rays, but they also will be brought to a focus at the other side of the lens at the point a. If the source of light A is moved nearer to the principal focus of the lens to a point A1 the rays will come to a focus at the point a1, and similarly when the light is at A2 the rays will come to a focus at the point a2. It can be found by direct experiment that the distance fa increases in the same proportion as AF diminishes, and diminishes in the same proportion as AF increases. The relationship which exists between pairs of points in this manner is termed the conjugate foci of a lens, and though every lens has only one principal focus, yet its conjugate foci are innumerable.
The formation of an image of some distant object in its principal focus is one of the most useful properties of a convex lens, and it is this property that forms the basis of several well-known optical instruments, including the camera, telescope, microscope, etc.
If we take an oblong wooden box, AA, and substitute a sheet of ground glass, C, for one end, and drill a small pinhole, H, in the centre of the other end opposite the