Aberrations
The simple equations, derived and discussed that connecting object and image distances, focal length etc. are based on the assumption that the angles made by the rays of light with the axis are small. In practice, however, lenses are used to form images of points situated off the axis also. Further, the cone of rays of light forming an image point is of finite size of the lens. In general non-paraxial rays of light from an object point do not meet at a single point after refraction through the lens. The refractive index and hence the focal length of a lens are different for different wavelengths of light. For a given lens, the refractive index for violet light is more than for red light. Thus, if the light coming from an object point is not monochromatic, a number of colored images are formed by the lens. These images, even though formed by paraxial rays, are at different positions and are of different sizes.
The deviations from the actual size, shape and positions of an image as calculated from the earlier simple equations, are called the aberrations produced by a lens. The aberrations produced by the variation of refractive index with wavelength of light are called chromatic aberrations. The other aberrations are caused even if monochromatic aberrations. Lens aberrations are just the consequence of the refraction laws at the spherical surfaces and not due to defective construction of a lens such as the surfaces being not spherical etc.
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