Manual

19
Method 3:
Set up a concave mirror behind the lens and a pin in front. An inverted image of the pin
will be seen on looking through the lens, and it may be made to coincide with the pin by suitably
adjusting the mirror.
Appendix 2: The Aberration of Lenses
Under ordinary circumstances, a lens or a system of lenses will not produce a perfect image. The
defects of the image arise in various ways from geometrical causes as well as from the physical
properties of glass, and they become especially troublesome when the lens is used at a large relative
aperture to cover a wide field of view. Except in unusual cases, lens designers are concerned with six
types of aberrations, two of which are briefly described below.
It is impossible to correct a system of lenses for all aberrations at the same time. Sometimes the process
of eliminating one defect intensifies another. Furthermore, a lens designed to give good images of
objects at one distance will give imperfect image at others. Hence it is impossible to design a
universally useful lens; each problem in lens design requires individual study. If an exceedingly sharp
image is required, the system needs especially fine spherical and chromatic correction; and this can
only be achieved by sacrificing the field of view to reduce the aberrations known as coma and
astigmatism. A wide-angle photographic lens, on the other hand, calls for freedom from coma and
astigmatism, and then the aperture of the lens must remain small to avoid spherical and chromatic
errors. This explains why wide-angle lenses rarely have relative apertures (values of D/f) greater than
1/10, while ordinary photographic lenses with smaller fields of view may have relative apertures as
high as 1/1.5.
Spherical Aberration:
This name is applied to the defect occurring in the image when the lens is large
and the object is on the axis of the lens, and light of only one color is used. It is a property of lenses
with spherical surfaces that rays from a point on the axis are not brought together at a single point
focus unless the lens has a very small relative aperture.
The magnitude of spherical aberration is proportional to the square of the relative aperture for lenses of
the same focal length, or to the focal length of the lenses of the same relative aperture. For all sorts of
lenses, the magnitude is proportional to the square of the diameter divided by the focal length. The
magnitude also varies with the shape of the lens. For a simple lens of 10cm diameter and 100cm focal
length (relative aperture 1/10), the magnitude is 1.67cm if the lens is symmetrically double-convex;
4.5cm if the lens is plano-convex with the plane side toward the distant object; and 1.17cm if the plane
side is turned toward the image.
It is possible to avoid, or at least reduce, this problem in three ways.
•
Reduce the diameter of the lens, or place a diaphragm in the beam near the lens so as to cut out all
but the central rays. The amount of light transmitted by the lens is then greatly reduced. This is
usually undesirable.
•
Choose a lens of the best shape by combining lenses of different shapes. It is possible to combine a
strongly convergent lens of a shape producing a small amount of aberration with a weaker
diverging lens, which gives the same aberration in the opposite direction without at the same time
completely annulling the convergence of the rays produced by the first lens.
•
Abandon the spherical surface and grind the lens to a slightly different shape. Aspherical lenses
are sometimes used in spectacles, microscopes and projection lanterns.
Chromatic Aberration: The bending of light by a lens varies with the color. A simple lens, if it had
no other defects, would bring the blue range of white light to a nearer focus than the red. The yellow