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The Gaussian Imaging Equation
(In accordance with the sign rules.) l l’ f Unfortunately, this equation is often (perhaps usually) written without regard to the sign rules: e.g., , where o and i refer to the ‘object’ and ‘image’ distance as always positive numbers. This leads to confusion and makes the correct equation harder to remember. Ignoring the sign rules works when considering a single, positive lens, but leads to confusion and errors when trying to trace a chain of intermediate images through an optical system. Ignoring the sign rules works when considering a single, positive lens, but leads to confusion and errors when trying to trace a chain of intermediate images through an optical system.
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Easy way to remember the Imaging Equation:
K=1/f l l’ At the lens, the incoming wave from the object point has curvature The lens adds curvature to the wave; So the outgoing wave has curvature , which is the correct equation. (Note that curvatures, like any other quantities, only add correctly if their signs are considered.
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