284 ABERRATION OF LENSES [Ch. IX 



passing through the center of the lens continues in a line parallel to 

 the original direction as it does in traversing a piece of plane glass 



(fig- 157)- 



As shown in the diagrams (fig. 167) the optic center is found by 

 drawing parallel radii from the two curved surfaces, or from the curved 

 and plane surface, and joining the ends of the radii. The center of 

 the lens is at the point where a line connecting the ends of the radii 

 crosses the principal axis (fig. 167, d). The reason why light rays 

 traversing the optic center have no angular deviation is evident, 

 for the radii are perpendicular to the surface of the lens, and the 

 tangent plane perpendicular to the radius is tangent to the sphere 

 at the end of the radius. As the tangents of two parallel radii must 

 themselves be parallel, it follows that a ray of Ught passing from one 

 tangential point to the other is traversing a body with parallel 

 sides at the point of entrance and exit, and hence it will suffer no 

 angular deviation. The ray may be displaced as in traversing any 

 thick transparent body (fig. 157). With meniscus lenses the optic 

 center (fig. 167, 8, 9) is on an extension of the line joining the centers 

 of curvature, and wholly outside the lens. 



(3) Secondary axis. This is any line which passes through the 

 ■optic center of the lens and is obUque to the principal axis. 



(4) Principal focal point. The principal focal point or focus of 

 a lens or of a lens system Hke an objective, a simple midroscope, etc., 

 is the point on the principal axis where rays of hght parallel to the 

 principal axis before entering the lens or lens system, cross the prin- 

 cipal axis after leaving the lens or objective (fig. 161-162). The 

 focus is also called the burning point. With a concave mirror it is 

 the point on the principal axis where rays parallel with the principal 

 axis before meeting the mirror, cross the principal axis after reflec- 

 tion from the concave surface. This point is situated half-way be- 

 tween the face of the mirror and the center of curvature. 



Aberration of Lenses 

 § 458. Spherical aberration. — This is a defect of spherical lenses 

 shown in fig. 168. That is, the parallel ray at the edge crosses the 

 principal axis or comes to a focus nearer the center of the lens than a 



