# Optical

## lens, center and axis

OPTICAL CENTER.—Every lens possesses a cer tain point, situated on its principal axis, termed the optical center. At this point every incident ray which passes through it does not undergo deviation, but pursues a path parallel to its original course.

Only single lenses have perfectly true optical centers in an achromatic combination; its position may be ascertained approximately by considering it as a single lens.

In order to obtain the optical center of a single lens, first draw a line B C B' (Fig. 29o). This to represent the principal axis. From the centers of curvatures B B' next draw two radii B'A and B A' parallel to each other, but oblique to the central axis B B'. Next join their ex tremities A A', and the point C where this line cuts the principal axis is the optical center. To obtain the optical center of a meniscus lens, prolong the line AA' to the point where it meets the principal axis, and this will be the optical center. In plano-convex and plano-concave lenses it is found by the inter-section of the spherical surfaces of the axis. The optical center of a plano-convex lens is on the

convex surface, and of a plano-concave on the concave sur face. If the lens be a meniscus or a concavo-convex, it will be outside the lens altogether, and its distance from the two surfaces will differ in proportion as their radii of curvature differ. The point C (Figs. 300 and 301) shows the position more clearly of the optical center of a plano-convex and a .meniscus. Another method of finding the optical center of the lens is the following: Let r be the radius of the front surface of a lens, s the radius of the back surface, and t the thickness of the lens, then the distance of the optical center, measured along the axis of the lens from the center of the face of the front sur surface, is equal to By giving to r and s the proper algebraical sign and a given magnitude, the position of the optical center of any lens may be easily found.