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Thermodynamics

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Optical Cardinal Points

In the case of refraction through a thin lens, the thickness of the lens has been neglected in calculating the various formulae. It is immaterial from which point of the lens the distances are measured. But in the case of a thick lens or in a combination of two lenses separated by a finite distance, we cannot proceed with this assumption. Moreover, the method of evaluating the distance of the image considering refraction at each surface fo a lens successively is extremely tedious. To overcome this difficulty, Gauss in 1841 proved that any number of co-axial refracting systems can be treated as one unit and the simple formulae for thin lenses can be applied, provided the distances are measured from two theoretical parallel planes, fixed with reference to the refracting system. The points of intersection of these planes with the axis are called the Principal or Gauss points. Actually, there are six points in all viz., the two principal, foci (focal points), the two principal points and the two nodal points, which are important in the case of refraction through a thick lens or in a system of co-axial lenses. These six points are known as cardinal points of an optical system.