Focal length

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 it converges (focuses) or diverges (diffuses) light. Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 A system with a shorter focal length has greater optical power than one with a long focal length. Optical power ( dioptric power or refractive power) is the degree to which a lens or Mirror converges or diverges light

1 Thin lens approximation
2 General optical systems
3 In photography
4 See also
5 References

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. In Optics, a thin lens is a lens with a thickness (distance along the Optical axis between the two surfaces of the lens that is negligible compared A lens is an optical device with perfect or approximate Axial symmetry which transmits and refracts Light, converging or diverging In Geometrical optics, a focus, also called an image point, is the point where Light rays originating from a point on the object converge. In Geometrical optics, a focus, also called an image point, is the point where Light rays originating from a point on the object converge. For a converging lens (for example a convex lens), the focal length is positive, and is the distance at which a beam of collimated light will be focused to a single spot. A lens is an optical device with perfect or approximate Axial symmetry which transmits and refracts Light, converging or diverging Collimated light is Light whose rays are nearly parallel and therefore will spread slowly as it propagates 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. A lens is an optical device with perfect or approximate Axial symmetry which transmits and refracts Light, converging or diverging

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. In Engineering, Mathematics, Physics and similar disciplines the term negligible refers to the quantities so small that they can be ignored (neglected g. , a photographic lens or a telescope), 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. A photographic lens (also known as objective lens or photographic objective) is an optical lens or assembly of lenses used in conjunction with A telescope is an instrument designed for the observation of remote objects and the collection of Electromagnetic radiation. The cardinal points and the associated cardinal planes are a set of special points and planes in an optical system which help in the analysis ^[1]
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. ^[1]

For an optical system in air, the effective focal length gives the distance from the front and rear principal planes to the corresponding focal points. The cardinal points and the associated cardinal planes are a set of special points and planes in an optical system which help in the analysis If the surrounding medium is not air, then the distance is multiplied by the refractive index of the medium. The refractive index (or index of Refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves is reduced inside the medium Some authors call this distance the front (rear) focal length, distinguishing it from the front (rear) focal distance, defined above. ^[1]

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. Magnification is the process of enlarging something only in appearance not in physical size The other parameters are used in determining where an image will be formed for a given object position. An image (from Latin imago) or picture is an artifact usually two-dimensional that has a similar appearance to some subject &mdashusually

For the case of a lens of thickness d in air, and surfaces with radii of curvature R₁ and R₂, the effective focal length f is given by:

$\frac{1}{f} = (n-1) \left[ \frac{1}{R_1} - \frac{1}{R_2} + \frac{(n-1)d}{n R_1 R_2} \right],$

where n is the refractive index of the lens medium. Radius of curvature has specific meaning and Sign convention in Optical design. The refractive index (or index of Refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves is reduced inside the medium The quantity 1/f is also known as the optical power of the lens. Optical power ( dioptric power or refractive power) is the degree to which a lens or Mirror converges or diverges light

The corresponding front focal distance is:

$\mbox{FFD} = f \left( 1 + \frac{ (n-1) d}{n R_2} \right),$

and the back focal distance:

$\mbox{BFD} = f \left( 1 - \frac{ (n-1) d}{n R_1} \right).$

In the sign convention used here, the value of R₁ will be positive if the first lens surface is convex, and negative if it is concave. In Physics, a sign convention is a choice of the signs (plus or minus of a set of quantities in a case where the choice of sign is arbitrary The value of R₂ 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. "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe A mirror is an object with a surface that has good Specular reflection; that is it is smooth enough to form an Image. Radius of curvature has specific meaning and Sign convention in Optical design. The focal length is positive for a concave mirror, and negative for a convex mirror. A curved mirror is a Mirror with a curved reflective surface which may be either convex (bulging outward or concave (bulging inward A curved mirror is a Mirror with a curved reflective surface which may be either convex (bulging outward or concave (bulging inward 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. Radius of curvature has specific meaning and Sign convention in Optical design.

In photography

How focal length affects photograph composition: adjusting the camera's distance from the main subject while changing focal length, the main subject can remain the same size, while the other at a different distance changes size.

When a photographic lens is set to "infinity", its rear nodal point is separated from the sensor or film, at the focal plane, by the lens's focal length. A photographic lens (also known as objective lens or photographic objective) is an optical lens or assembly of lenses used in conjunction with The cardinal points and the associated cardinal planes are a set of special points and planes in an optical system which help in the analysis The cardinal points and the associated cardinal planes are a set of special points and planes in an optical system which help in the analysis 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. The pinhole camera model describes the mathematical relationship between the coordinates of a 3D point and its Projection onto the image plane of an ideal Pinhole Combining this definition with an assumption of rectilinear imaging (that is, with no image distortion) leads to a simple geometric model the photographers use for computing the angle of view of a camera. In Photography, angle of view describes the angular extent of a given scene that is imaged by 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 a 35 mm camera with a focal length of $f = 50 mm$ . In Photography and Cinematography a normal lens is a lens that generates images that generally look "natural" to a human observer under normal 35 mm film is the basic Film gauge most commonly used for both still Photography and Motion pictures, and remains relatively unchanged since its To focus a distant object ( $S_1\approx \infty$ ), the rear nodal point of the lens must be located a distance $S 2 = 50 mm$ from the image plane. To focus an object 1 m away ( $S 1 = 1000 mm$ ), the lens must be moved 2. 6 mm further away from the image plane, to $S 2 = 52. 6 mm$ .

Note that some simple and usually inexpensive cameras have fixed focus lenses which cannot be adjusted. A fixed-focus lens is a lens of which the focus is not adjustable

Focal lengths are usually specified in millimetres (mm), but older lenses marked in centimetres (cm) and inches are still to be found. The Millimetre ( American spelling: millimeter, symbol mm) is a unit of Length in the Metric system, equal to A centimetre ( American spelling: centimeter, symbol cm) is a unit of Length in the Metric system, equal to one hundredth Inches redirects here To see the Les Savy Fav album see Inches. The angle of view depends on the ratio between the focal length and the film size. In Photography, angle of view describes the angular extent of a given scene that is imaged by a Camera. A film format is a technical definition of a set of standard characteristics regarding image capture on Photographic film, for either stills or movies

A lens with a focal length about equal to the diagonal size of the film or sensor format is known as a normal lens; its angle 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;^[2] this angle of view is about 53 degrees diagonally. In Photography and Cinematography a normal lens is a lens that generates images that generally look "natural" to a human observer under normal In Photography, angle of view describes the angular extent of a given scene that is imaged by a Camera. 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 a wide-angle lens (typically 35 mm and less, for 35mm-format cameras), while a lens significantly longer than normal may be referred to as a telephoto 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 same angle of view, or field of view, if used on a full-frame 35 mm camera. In Photography, the 35 mm equivalent focal length is a measure that indicates the Angle of view of a particular combination of a camera lens In Photography, angle of view describes the angular extent of a given scene that is imaged by a Camera. A full-frame digital SLR is a Digital single-lens reflex camera (DSLR fitted with an Image sensor that is the same size as a 35 mm (36x24 mm film frame Use of a 35 mm equivalent focal length is particularly common with digital cameras, 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 the crop factor. Many compact digital still cameras can record Sound and moving Video as well as still Photograph. In Digital photography, a crop factor is the ratio of the dimensions of a camera's imaging area compared to a reference format most often this term is applied to

References

^ ^a ^b ^c Greivenkamp (2004). In Optics, particularly as it relates to Film and Photography, the depth of field (DOF is the portion of a scene that appears sharp in the image A dioptre, or diopter, is a Unit of measurement of the Optical power of a lens or curved Mirror, which is equal to the reciprocal In Geometrical optics, a focus, also called an image point, is the point where Light rays originating from a point on the object converge.
^ Leslie D. Stroebel (1999). View Camera Technique. Focal Press.

Grievenkamp, John E. (2004). Field Guide to Geometrical Optics, SPIE Field Guides vol. FG01, SPIE. ISBN 0-8194-5294-7.
Hecht, Eugene (2001). Optics, 4th ed. , Pearson Education. ISBN 0-8053-8566-5.

Dictionary

-noun

(optics) The distance at which something (e.g. a lens, mirror etc.) is in focus; distance along the optical axis from the lens to the focus or focal point.

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