Spherical aberration is caused because light rays enter the element of a lens not only at the center but also through the edges. They therefore get focused at different points. Spherical aberration can be easily controlled by corrections made at the designing stage and is today virtually absent in multi element lens. Stopping the lens down will also reduce spherical aberration.
For lenses made with spherical surfaces, rays which are parallel to the
optic axis but at different distances from the optic axis fail to converge
to the same point. For a single lens, spherical aberration can be minimized
by bending the lens into its best form. For multiple
lenses, spherical aberrations can be canceled by overcorrecting some
elements. The use of symmetric doublets greatly reduces spherical
aberration.
Other than distortions from lens imperfections, certain distortions occur from the geometry of the lens. The barrel and pincushion distortions below can be readily seen in the image formed by a thick double convex glass lens.
Barrel distortion is when a square is reproduced as a barrel shape with
the sides bowing outwards (wide angle lenses)
Pincushion distortion is where a square is reproduced in a pincushion shape
with the sides bowing inwards. (telephoto lenses)
Zoom lenses may exhibit both barrel distortion at the wide angle end and
pincushion at the telephoto end.
They are the reason for a practical limitation in the magnification achievable from a simple magnifier. These distortions are mimimized by using symmetric doublets such as the orthoscopic doublet and eyepieces such as the Ramsden eyepiece.
A lens will not focus different colors in exactly the same place because the focal length depends on refraction and the index of refraction for blue light (short wavelengths) is larger than that of red light (long wavelengths). The amount of chromatic aberration depends on the dispersion of the glass.