Third Order Theory
If, in the formulae for reflection and refraction at spherical surfaces the first two terms of the series are replaced for values of sines of angles, the results obtained represent the third order theory. The formulae thus obtained give a fairly accurate account of the principal aberrations. In the third order theory, the aberration of a ray of light viz. its deviations from the path obtained from Gauss formulae, is denoted by five sums called the Seidel sums. A lens will be free from all the aberrations, if all the five sums are equal to zero, but, in practice, no optical system can be made to satisfy all the conditions at the same time. Let, S1, S2 etc. denote the five Seidel sums. Then, spherical aberration is absent if S1 = 0; coma is absent if S1 = 0, S2 = 0, S3 = 0 and S4 = 0. Finally, if S5 is also equal to zero the images of an axial object will be free from distortion as well. These five defects of an image are called the monochromatic aberrations.
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