172 OPTICAL PRINCIPLES. 



they are divergent, as in PL XII. fig. 16, the focus/will 

 be situated further from the lens than the principal 

 focus o. By concave lenses the incident rays are ren- 

 dered divergent, as in PL XII. fig. 17, as if they ema- 

 nated from a point /, situated on the same side of the 

 lens as that upon which the rays are incident, and 

 called the virtual focus. 



Spherical aberration. Although, as a general ex- 

 pression, we have stated that the rays of light meet 

 at a focus on passing through a convex lens, this is 

 not strictly correct. For, in ordinary convex lenses, 

 the marginal rays are more refracted than the central 

 ones, and meet at focal points nearer the lens than the 

 latter, as shown in PL "XII. fig. 18. This important 

 defect is called spherical aberration, and arises from 

 the lateral rays being incident upon more oblique 

 portions of the curved surface of the lens than the 

 central rays. Hence objects seen through such lenses 

 appear misty and confused, the central and lateral 

 parts of a flat object not being visible at the same 

 time ; and even when the marginal parts are visible, 

 they appear distorted or deformed. 



Spherical aberration is greatest in the most convex 

 lenses ; and, in a plano-convex lens, it is least when 

 parallel rays enter at or emerge from its convex sur- 

 face. 



In certain lenses, the convex surface of which has 

 the form of a parabola, a hyperbola, or an ellipse, 

 the spherical aberration is absent; but it is impos- 

 sible to grind microscopic lenses of these forms with 

 absolute accuracy, so that the fact is of no practical 

 value. 



The form of simple convex lens most free from 

 aberration is that in which the curves of the two sur- 

 faces form parts of a sphere, the radii of the curves 

 being as 1 to 6; the focal length being rather less 

 than twice the length of the radius of the most con- 

 vex surface. This form of lens comes very near to 



