In Section 1.8.3, we considered Gaussian imaging by a reflecting surface, and showed that the curved surface can be replaced by a planar surface that is a tangent to the surface at its vertex, called the tangent plane or the paraxial surface. In this chapter, we rederive the Gaussian imaging equations for a spherical reflecting surface and show that they can be obtained from those for a corresponding refracting surface by substituting the refractive index associated with the reflected rays equal to the negative value of that associated with the incident rays. Both Gaussian and Newtonian forms of the imaging equations are given. We also show how to determine the image graphically. The Petzval image, two-mirror telescopes, a beam expander, and the image displacement resulting from the misalignment of a mirror are also discussed.
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