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Extra resources for Science for the Curious Photographer: An Introduction to the Science of Photography
Sample text
This is called the paraxial approximation with which Snell’s law becomes n1θ1 ϭ n2θ2. With the paraxial approximation it is easy to derive equations for a simple thin lens. 1 is defined as Ps ϭ (n2 – n1)/R, and our first goal is to relate this power to the object and image distances p and q, respectively. 2. 1 because the center of curvature is on the extreme right-hand side, and the radius of the second (exit) surface R2 is less than zero because its center of curvature is far on the left-hand side.
Rays parallel to the optical axis pass, after refraction, through the focal point (F2 ) of the lens. 1. Image creation with a simple lens. Of course, this works in both directions, so a ray passing through a focal point will, after refraction, emerge parallel to the optical axis. These rules suffice for determining the magnification m ϭ image/ object ϭ q͞p and also for deriving the conjugate equation 1͞p + 1͞q ϭ 1͞f. With this lens there is no ambiguity. The distances are well defined, and, if a stop (aperture) is added, it will certainly be very close to the front or rear surface of the lens.
4, is such an obvious characteristic of a simple lens that some opticians do not even regard it as an aberration. 4. An illustration of image curvature. This curvature is, in fact, a unique kind of aberration because it does not depend on the aperture, or other characteristic distances in compound lenses. It does, however, depend on the focusing powers of the optical surfaces, and in 1839 Joseph Petzval (1807–1891) derived an equation for the field curvature expected from a compound lens with a number of optical surfaces in the absence of other aberrations.