As S 1 {\displaystyle S_{1}} is decreased, S 2 {\displaystyle S_{2}} must be increased. For example, consider a normal lens for a 35 mm camera with a focal length of f = 50  mm {\displaystyle f=50{\text{ mm}}} . To focus a distant object ( S 1 ≈ ∞ {\displaystyle S_{1}\approx \infty } ), the rear nodal point of the lens must be located a distance S 2 = 50  mm {\displaystyle S_{2}=50{\text{ mm}}} from the image plane. To focus an object 1 m away ( S 1 = 1000  mm {\displaystyle S_{1}=1000{\text{ mm}}} ), the lens must be moved 2.6 mm further away from the image plane, to S 2 = 52.6  mm {\displaystyle S_{2}=52.6{\text{ mm}}} .

Is focal lengthpositive ornegativein concave mirror

Supponiamo ora di racchiudere i nostri atomi all'interno di una cavità ottica delimitata da due specchi: in questo caso la luce prodotta per emissione stimolata si propaga nella direzione ortogonale agli specchi (raggi gialli in fig. c) e continua a rimbalzare fra i due specchi, venendo amplificata ad ogni passaggio. Se il numero di atomi eccitati è sufficientemente elevato, l'amplificazione supera le inevitabili perdite del sistema e si dice che il laser oscilla. Se ora uno dei due specchi è reso parzialmente trasparente alla luce emessa dagli atomi, attraverso di esso sarà possibile estrarre un fascio laser. L'emissione laser è dunque fondamentalmente basata sul fenomeno dell'emissione stimolata già previsto da Einstein nel 1917, e ciò rende tale luce di natura completamente diversa da quella emessa dalle comuni lampadine. Lo schema generale di un laser è rappresentato in fig. c. Gli atomi eccitati del materiale cosiddetto attivo producono l'emissione stimolata. L'eccitazione avviene mediante un meccanismo opportuno (elettrico od ottico), indicato come pompaggio nella figura. I due specchi terminali possono essere piani o, più comunemente, sferici. Il materiale attivo può trovarsi in diverse forme: gassosa (laser a gas), liquida (come avviene nei laser a colorante organico), di monocristalli massicci (laser a stato solido), di materiale semiconduttore (laser a semiconduttore).

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. 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.

Al momento della sua invenzione il laser fu definito "una brillante soluzione in cerca di un problema". Oggi, cinquantuno anni dopo, poche tecnologie trovano, quanto i laser, una così ampia applicazione in ambito scientifico e tecnologico, essendo inoltre ancora oggetto di intenso sviluppo. L'estrema versatilità del laser nasce dall'ampio intervallo di lunghezze d'onda e di potenza, nonché dalla possibilità di avere emissione laser con diverse caratteristiche temporali, dal regime continuo agli impulsi ultracorti. Le principali applicazioni si rivolgono ai settori delle telecomunicazioni, delle lavorazioni meccaniche, della biomedicina, del monitoraggio ambientale, della conservazione dei beni culturali, della sensoristica e della sicurezza. Il laser è un eccellente strumento di lettura: basti pensare ai lettori di codici a barre nei supermercati, ai lettori di compact disc, DVD e blu-ray. È un ottimo strumento di taglio e di marcatura, sia per lavorazioni industriali (p. es. taglio di lamiere) che per applicazioni mediche di altissima precisione (chirurgia laser, p. es. per la correzione della miopia). Il laser, quindi, è una tecnologia che è entrata a pieno titolo in molti aspetti della nostra vita quotidiana. Ma quali sono i suoi principi di funzionamento? I laser (acronimo di light amplification by stimulated emission of radiation) sono sorgenti di radiazione elettromagnetica con frequenza che va dai raggi X alle microonde (e in quest'ultimo caso vengono chiamati maser, da microwave), con caratteristiche particolari di monocromaticità, direzionalità, coerenza e brillanza (vd. approfondimento). Si basano, come dice il nome, sull'amplificazione della luce mediante emissione stimolata di radiazione.

Focal lengthof convex lensispositive ornegative

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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 a concave mirror, and negative for a convex mirror. In the sign convention used in optical design, a concave mirror has negative radius of curvature, so

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When is focal length negativein mirror

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 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.

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. 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.

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Focal lengthof concave lensispositive ornegative

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. If the surrounding medium is not air, then the distance is multiplied by the refractive index of the medium. Some authors call this distance the front (rear) focal length, distinguishing it from the front (rear) focal distance,\, defined above.[1]

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 {\displaystyle f} , the distance from the front nodal point to the object to photograph S 1 {\displaystyle S_{1}} , and the distance from the rear nodal point to the image plane S 2 {\displaystyle S_{2}} are then related by:

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 of collimated 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.

Negative focal lengthreal or virtual

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:

When isimage distancenegative

Knowledge of this property is useful for the construction of various optical devices, such as eyeglasses, cameras, telescopes, and microscopes.

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Focal length

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 an image will be formed for a given object position.

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;[3] 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 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.

The focal length of an optical system is a property that provides a measure of how strongly the system converges (focuses) or diverges (diffuses) light. The optical system may consist of a lens or mirror or some combination of lenses and mirrors. A system with a shorter focal length has greater optical power than one with a long focal length.

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Focal lengthof convex mirrorispositive ornegative

201465 — A reticle design is disclosed for use in the first focal plane, which can be used both for close range and long range shooting.

Focal lengths are usually specified in millimeters (mm), but older lenses marked in centimeters (cm) and inches are still to be found. The angle of view depends on the ratio between the focal length and the film size.

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Biografia Orazio Svelto è professore del Politecnico di Milano. È considerato uno dei pionieri internazionali per le scienze e le applicazioni dei laser. In questo settore ha pubblicato oltre 200 lavori su riviste internazionali ed è anche autore del libro Principles of Lasers, pubblicato dalla casa editrice Springer di New York, attualmente alla sua quinta edizione.

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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. 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.

For a thick lens (one which has a non-negligible thickness), or an imaging system consisting of several lenses and/or mirrors (e.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:

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