- Focal length
The

**focal length**of an optical system is a measure of how strongly it converges (focuses) or diverges (diffuses)light . A system with a shorter focal length has greateroptical power than one with a long focal length.**Thin lens approximation**For a

thin lens in air, the focal length is the distance from the center of the lens to the principal foci (or focal points) of the lens. For a converging lens (for example a convex lens), the focal length is positive, and is the distance at which a beam ofcollimated light will be focused to a single spot. For a diverging lens (for example a concave lens), the focal length is negative, and is the distance to the point from which a collimated beam appears to be diverging after passing through the lens.**General optical systems**For a "thick lens" (one which has a non-

negligible thickness), or an imaging system consisting of several lenses and/or mirrors (e.g., aphotographic lens or atelescope ), the focal length is often called the**effective focal length**(EFL), to distinguish it from other commonly-used parameters:

***Front focal length**(FFL) or**Front focal distance**(FFD) is the distance from the front focal point of the system to the vertex of the "first optical surface".

***Back focal length**(BFL) or**Back focal distance**(BFD) is the distance from the vertex of the "last optical surface" of the system to the rear focal point.For an optical system in air, the effective focal length gives the distance from the front and rear

principal plane s to the corresponding focal points. If the surrounding medium is not air, then the distance is multiplied by therefractive index of the medium. Some authors call this distance the front (rear) focal length, distinguishing it from the front (rear) focal "distance", defined above.Greivenkamp (2004).]In general, the focal length or EFL is the value that describes the ability of the optical system to focus light, and is the value used to calculate the

magnification of the system. The other parameters are used in determining where animage will be formed for a given object position.For the case of a lens of thickness "d" in air, and surfaces with radii of curvature "R"

_{1}and "R"_{2}, the effective focal length "f" is given by::$frac\{1\}\{f\}\; =\; (n-1)\; left\; [\; frac\{1\}\{R\_1\}\; -\; frac\{1\}\{R\_2\}\; +\; frac\{(n-1)d\}\{n\; R\_1\; R\_2\}\; ight]\; ,$where "n" is the

refractive index of the lens medium. The quantity 1/"f" is also known as theoptical power of the lens.The corresponding front focal distance is::$mbox\{FFD\}\; =\; f\; left(\; 1\; +\; frac\{\; (n-1)\; d\}\{n\; R\_2\}\; ight),$and the back focal distance::$mbox\{BFD\}\; =\; f\; left(\; 1\; -\; frac\{\; (n-1)\; d\}\{n\; R\_1\}\; ight).$

In the

sign convention used here, the value of "R"_{1}will be positive if the first lens surface is convex, and negative if it is concave. The value of "R"_{2}is positive if the second surface is concave, and negative if convex. Note that sign conventions vary between different authors, which results in different forms of these equations depending on the convention used.For a spherically curved

mirror in air, the magnitude of the focal length is equal to the radius of curvature of the mirror divided by two. The focal length is positive for aconcave mirror , and negative for aconvex mirror . In the sign convention used in optical design, a concave mirror has negative radius of curvature, so :$f\; =\; -\{R\; over\; 2\}$,where $R$ is the radius of curvature of the mirror's surface.

See

Radius of curvature (optics) for more information on the sign convention for radius of curvature used here.**In photography**When a

photographic lens is set to "infinity", its rearnodal point is separated from the sensor or film, at thefocal plane , by the lens's focal length. Objects far away from the camera then produce sharp images on the sensor or film, which is also at the image plane. Photographers sometimes refer to the image plane as the focal plane; these planes coincide when the object is at infinity, but for closer objects the focal plane is fixed, relative to the lens, and the image plane moves, by the standard optical definitions.The focal length of a lens determines the magnification at which it images distant objects. The focal length of a lens is equal to the distance between the image plane and a pinhole (see

pinhole camera model ) that images distant small objects the same size as the lens in question. Combining this definition with an assumption ofrectilinear imaging (that is, with noimage distortion ) leads to a simple geometric model the photographers use for computing theangle of view of a camera.To render closer objects in sharp focus, the lens must be adjusted to increase the distance between the rear nodal point and the film, to put the film at the image plane. The focal length $f$, the distance from the front nodal point to the object to photograph $S\_1$, and the distance from the rear nodal point to the image plane $S\_2$ are then related by:

:$frac\{1\}\{S\_1\}\; +\; frac\{1\}\{S\_2\}\; =\; frac\{1\}\{f\}$.

As $S\_1$ is decreased, $S\_2$ must be increased. For example, consider a

normal lens for a35 mm camera with a focal length of $f=50\; ext\{\; mm\}$. To focus a distant object ($S\_1approx\; infty$), the rear nodal point of the lens must be located a distance $S\_2=50\; ext\{\; mm\}$ from the image plane. To focus an object 1 m away ($S\_1=1000\; ext\{\; mm\}$), the lens must be moved 2.6 mm further away from the image plane, to $S\_2=52.6\; ext\{\; mm\}$.Note that some simple and usually inexpensive cameras have

fixed focus lenses which cannot be adjusted.Focal lengths are usually specified in

millimetre s (mm), but older lenses marked incentimetre s (cm) andinch es are still to be found. Theangle of view depends on the ratio between the focal length and the film size.A lens with a focal length about equal to the diagonal size of the film or sensor format is known as a

normal lens ; itsangle of view is similar to the angle subtended by a large-enough print viewed at a typical viewing distance of the print diagonal, which therefore yields a normal perspective when viewing the print; [*cite book | title = View Camera Technique | author = Leslie D. Stroebel | publisher = Focal Press | year = 1999 | ibsn = 0240803450 | url = http://books.google.com/books?id=71zxDuunAvMC&pg=PA136&dq=appear-normal+focal-length-lens+print-size+diagonal+viewer+distance&lr=&as_brr=3&ei=x8L3R6mMJI-KswPRspyFCg&sig=X65o2ElkUmnoebKyKOIZR7Z0y1I*] this angle of view is about 53 degrees diagonally. For full-frame 35mm-format cameras, the diagonal is 43 mm and a typical "normal" lens has a 50 mm focal length. A lens with a focal length shorter than normal is often referred to as awide-angle lens (typically 35 mm and less, for 35mm-format cameras), while a lens significantly longer than normal may be referred to as atelephoto lens (typically 85 mm and more, for 35mm-format cameras), though the use of the term is inaccurate as it implies specific optical design qualities that may or may not apply to a given lens.Due to the popularity of the 35 mm standard, camera–lens combinations are often described in terms of their

35 mm equivalent focal length , that is, the focal length of a lens that would have the sameangle of view , or field of view, if used on a full-frame 35 mm camera. Use of a 35 mm equivalent focal length is particularly common withdigital camera s, which often use sensors smaller than 35 mm film, and so require correspondingly shorter focal lengths to achieve a given angle of view, by a factor known as thecrop factor .**See also***

Depth of field

*f-number or focal ratio

*Dioptre

*Focus (optics) **References***

* cite book

last = Hecht | first = Eugene

title = Optics

edition = 4th ed.

publisher = Pearson Education

year = 2001

id = ISBN 0-8053-8566-5

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2010.*