# Focal length

the focal length ([itex] f< /math> ) the distance of a focus is in the optics ([itex] F< /math> also focus mentioned) of it assigned the main point ([itex] H< /math>) on the lens or the hollow mirror with parallel breaking in light.

[itex] f= \ bar {HF}< /math>

## Brechwert

the reciprocal value of the focal length (related to air) is called Brechwert D:

[itex] D = \ frac {1} {f}< /math>

The Brechwert possesses therefore the unit 1/Meter. This unit becomes (only in connection with a Brechwert) also diopter (abbreviation: dpt) mentioned.

Example: A free standing lens of the focal length 10 cm = 0.10 m (meters) has the Brechwert of 1 (0.10 m)= 10 dpt. Optical system, which has light in one point, which focus combines, a focal length. With a thin lens the focal length is into approximately the distance of the focus of the lens. The focal length specifies the distance that more accurately Main level of the lens of the focus.

If lenses are closely successively combined, adds itself the Brechwerte of the Einzellinsen with consideration of the sign for collecting and/or. Streulinsen

[itex] \ frac {1} {f_+} + \ frac {1} {f_} = \ frac {1} {f_S}< /math>

whereby f + and f - the focal lengths of a collecting and/or. Scatter lensdesignate and f S the focal length of the system represent.

With different optical systems the focal length cannot be measured directly from the distance between objective and image plane. It acts around systems, with those the path of rays after passing of theObjective one fans out again, e.g. with zooms, with employment of a Barlow lens or with mirror lenses in the design Schmidt Cassegrain or Maksutov.

## dependence on the form

the connection between nugget shape and focal length gives the so-called Linsenschleiferformelon. Here it is only marked that:

• with a collecting lens (also convex lens) the sunlight to be in such a way concentrated can that z. B. Paper due to the high intensity of the bundled light to burn begins. Therefore the terms actually agitate focal length and Focus.
• a scatter lens (also concave lens) a virtual (negative) focal length has.

With a spherical lens the focal length in the central site varies to the one boundary region (spherical aberration). In order to adjust and the picture place the focal length difference clearly, there is several possibilities. In addition count: (Only the middle part of the lens dip the headlights used), use of lens combinations, which adjust the error, use of aspheric lenses or mirrors (e.g.Parabolic reflector).

## dependence on the color (wavelength)

there the strength that Refraction of the refractive index [itex] n< /math> , this depends medium again on <the propagation speed> math c_ {}< /math> the wave in the appropriate medium and [itex] c_ {medium}< /math> of the wavelength ([itex] \ hat=< /math> Color of the light) depends, arises for different colors a different Brechwert. Briefly expressed:

[itex] n = \ frac {c_0} {c_ {medium}}\; [/itex] and [itex] \; \ lambda= \ frac {c_ {medium}} {f_w} \; [/itex] [itex] \; \ Rightarrow \; n = \ frac {c_0} {\ lambda \ f_w} \; [/itex] whereby [itex] c_0 [/itex] for the speed of light in the vacuum and [itex] f_w< /math> for the frequency of the wave stands.

The different change of the wavelength of electromagnetic waves in the mediumwith continuous frequency it causes finally the refraction differences between the different colors why aberrations, like color fringings or indistinct places on black-and-white pictures, can develop.

For adjusting one can use achromatic or apochromatische lens combinations of special Gläsern.

## focal length regulation

thoseFocal length of a lens can be computed from the Linsengleichung, if article and image intercept admit are. Elaboriertere measuring procedures are the Bessel procedure and the Abbe procedure.

## focal length data with digital cameras

the comparison with 35mm cameras becomes often additional with digital cameras oralternatively to the actual focal length of the objective the focal length indicated, which results in the same picture angle at the small display format (24 mm × 36 mm ).

By the far spreading of the small display format did not become the organization into telephoto, normal objective and wide angle (like it actually correctly) the picture angle would have consulted, but the focal length. The picture angle changes however, if with same focal length the size of the photo-sensitive surface ( the photograph format) is changed. The photo-sensitive surface with digital cameras is mostly smaller than the small display format, the picture angleis likewise smaller therefore.

For this effect with digital mirror reflex cameras the misleading term focal length extension was in-patriated. For the cameras an alleged focal length extension factor is indicated, which is to make a simple comparison possible with the small display format.