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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.
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 ...
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.
The ray transfer equation thus ... For the example of free space of length d followed by a lens of focal length f: ... f = focal length of lens where f > 0 for convex ...
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 camera equation, or G#, is the ratio of the radiance reaching the camera sensor to the irradiance on the focal plane of the camera lens. [8] The maximum usable aperture of a lens is specified as the focal ratio or f-number, defined as the lens's focal length divided by the effective aperture (or entrance pupil), a dimensionless number. The ...
Similarly to curved mirrors, thin lenses follow a simple equation that determines the location of the images given a particular focal length and object distance (): + = where is the distance associated with the image and is considered by convention to be negative if on the same side of the lens as the object and positive if on the opposite side ...