at /. In the same manner will the rays which enter 

 between c h and / d come together at intermediate 

 points between o and /, and those of the central portion 

 between h and / will fall beyond /. Spherical aberra- 

 tion increases with the decrease in the focus of a lens 

 and in lenses of the same focus but different form, is 

 greatest in the double convex and least in the so-called 

 crossed lens, in which the two convex surfaces are of 

 different radii and in the proportion of i to 6, on 

 condition, however, that the surface of shorter radius is 

 directed toward the object. 



This latter form of magnifying lens is seldom used, 

 as it shows the greatest amount of aberration if used in 

 the reversed position. The most common form is the 

 double convex with equal curvatures and when con- 

 siderable magnifying power is desired, the defects of 

 spherical aberration are partially overcome by the 

 interposition of an opaque plate, with round opening, 

 to shut out the marginal rays. This plate is called 

 a diaphragm and when used the lens is said to be 

 stopped down. 



Chromatic Aberration. In magnifying an object 

 with a single lens it will be noticed that it has not only 

 the defect of spherical aberration, but that the object 

 appears fringed with colors, predominantly violet and 

 red, or if objects are viewed through a prism, we have 

 not only an apparent change of position, but a decided 



