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Every optical system has six important points, called cardinal points, associated with, and inherent in, the system. These are two principal focal points, F1 and F2, two principal points, P1 and P2, and two nodal points, N1 and N2. In the simplest optical system, such as a curved spherical mirror, these six cardinal points are reduced to three, as each pair of points coincide; i. e., F1 coincides with F2, P1 with P2 and N1 with N2. In a slightly more complex optical system, such as a single refracting surface, the six cardinal points are reduced to four, as two pairs of points coincide, i. e., P1 with P2 and N1 with N2. In a lens situated in air, the six cardinal points also are reduced to four but by a different kind of coincidence.
Pascal JI. A MEMORY SCHEME FOR THE CARDINAL POINTS. Arch Ophthalmol. 1939;22(3):448–449. doi:https://doi.org/10.1001/archopht.1939.00860090114014
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