Page:Elementary Text-book of Physics (Anthony, 1897).djvu/432

418 If we draw $$AB,$$ cutting the axis at $$O,$$ the triangle $$CAO, C'BO$$ are similar, and $$\frac{CA}{C'B} = \frac{CO}{C'O}\cdot$$ But $$\frac{CA}{C'B},$$ being the ratio of the radii, is constant for all parts of the surfaces, hence $$\frac{CO}{C'O}$$ must be constant, or all lines such as $$AB$$ must cut the axis at one point $$O.$$ $$O$$is the optical centre, and light passing through it is not deviated by the lens.

341. Geometrical Construction of Images.—For the geometrical construction of images formed by curved surfaces, it is convenient to use, in place of the waves themselves, lines perpendicular to the wave front, which represent the paths which the light follows, and are called rays of light. These rays, when perpendicular to a plane wave surface, are parallel, and an assemblage of such rays, limited by an aperture in a screen, is called a beam. When the rays are perpendicular to a spherical wave surface, they pass through the wave centre, and constitute a pencil.

A plane wave surface perpendicular to the axis of a lens is converted by the lens into a spherical wave surface with its centre at the principal focus. The rays perpendicular to the plane wave surface are parallel to the axis, and after emergence must all pass through the principal focus. . Conversely, rays emanating from the principal focus emerge from the lens as rays parallel to the axis. Also, rays emanating from any focus must, after emerging from the lens, meet at the conjugate focus. Let $$L,$$ Fig. 108, be a converging lens, and $$AB$$ an object. Let be the optical centre, and $$F$$ the principal focus. Since all the rays from $$A$$ must meet, after emerging from the lens, at the conjugate focus, which is the image of $$A,$$ to find the position of the image it is only necessary to draw two such rays and find their intersection. The ray through the optical centre is not deviated, and the straight line $$AA'$$ represents both the incident and emergent rays. The ray $$AL$$ may be