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The focal point F and focal length f of a positive (convex) lens, a negative (concave) lens, a concave mirror, and a convex mirror.. The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power.
Thin lens equation f = lens focal length; x 1 = object distance; x 2 = image distance; r 1 = incident curvature radius; r 2 = refracted curvature radius
For a single lens surrounded by a medium of refractive index n = 1, the locations of the principal points H and H ′ with respect to the respective lens vertices are given by the formulas = ′ = (), where f is the focal length of the lens, d is its thickness, and r 1 and r 2 are the radii of curvature of its surfaces. Positive signs indicate ...
The signs are reversed for the back surface of the lens: R 2 is positive if the surface is concave, and negative if it is convex. This is an arbitrary sign convention; some authors choose different signs for the radii, which changes the equation for the focal length. For a thin lens, d is much smaller than one of the radii of curvature (either ...
For the purposes of ray tracing, this is equivalent to a series of identical thin lenses of focal length f = R/2, each separated from the next by length d. This construction is known as a lens equivalent duct or lens equivalent waveguide.
The reciprocal of the focal length, , is the optical power of the lens. If the focal length is in metres, this gives the optical power in dioptres (reciprocal metres). Lenses have the same focal length when light travels from the back to the front as when light goes from the front to the back.
If the lens is held at a distance from the object such that its front focal point is on the object being viewed, the relaxed eye (focused to infinity) can view the image with angular magnification = Here, is the focal length of the lens in centimeters. The constant 25 cm is an estimate of the "near point" distance of the eye—the closest ...
For optics like convex lenses, the converging point of the light exiting the lens is on the input side of the focal plane, and is positive in optical power. For concave lenses, the focal point is on the back side of the lens, or the output side of the focal plane, and is negative in power.