Focal Distance

The focal distances , respectively object and image, from a convergent centered optical system or diverge are, by definition, the algebraic distances respectively separating the plan main object from the hearth object and the principal plan image of the hearth image. They are often noted respectively ƒ and ƒ ′.

In the case of a mean system , for example a thin lens, the principal plans can be confused with the optical Center of the lens and in this case the focal distance image is easily defined by the algebraic distance separating the optical center from the thin lens of the hearth image.

In all the cases the focal distances belong to the cardinal elements of a system, i.e. of a whole of sizes which allow a complete definition of the system and an easy digitalization of calculation, in particular in matric Optique.

Properties

For the optical systems whose mediums of entry and exit are identical, the focal distances become equal in absolute value. It is the very traditional case of a lens plunged in the air for which $H' F'=-HF=f'=-f$ .

One easily includes/understands this property starting from an other possible definition of the focal distances, starting from the Vergence $V$ of a system. If one calls $n$ and $n'$ the indices of entry and exit of the system:

$f'= \ frac {} {V}$ and $f=- \ frac {N} {V}$

For the systems plunged in the air (for example in photography) one thus finds also the following property: the focal distance image is the reverse of vergency:

$f'=-f= \ frac {1} {V}$

The concept of convergence and divergence is some also clarified: one will call converge an optical system whose focal distance image is positive and divergent a system whose focal distance image is negative. A convergent lens has a positive focal distance and a divergent lens a negative focal distance. In photography, the objectives are convergent systems as well as the caps of approach. The lapping machines of focal distance which one intercalates between the objective and film or (the sensor) are afocaux systems.

Calculation and measurement

It is always possible to calculate the focal distances starting from the geometrical data and of the indices of a system (curve, Index of refraction) since they are connected to the Vergence. Nevertheless when these data have suddenly missed an experimental measurement is possible.

Experimental measurements, for the mean systems the such thin lenses, generally rest on the determination of the positions of the hearths object and image. It is pointed out that the hearth image is the point towards which converge after the system of the rays which are parallel to the optical axis before the system. Contrary, rays passing by the hearth object arise parallel with the optical axis. The rays do not pass necessarily physically by the hearth, it can act of their prolongation.

One can have the illustration in some simple cases of it:

optical Lens;
Mirror curve.

One can also measure it in several ways in experiments:

By measuring it directly between the lens and the clear image of a sufficiently remote object to be regarded as ad infinitum (sun, stars or landscape at the horizon).
With the method known as of Silbermann: when the lens is placed in such way that the image on a screen (real image) with the same size as the object then the distance between the image and the object is worth four times the focal distance.
By the method of Autocollimation (for the convergent lenses only): after having joined a plane mirror with a lens, it is enough to seek the position of the lens for which object and image are superimposed perfectly. The distance between the object and the lens is then the focal distance from this lens.

Photography

Significant surface (the film in the case of the silver Photography, the sensor in the case of the Numeric photography) is in the plan of convergence of the rays resulting from the object to be photographed (see the articles Mise at the point and Depth of field ). In the case of an object “ad infinitum” (i.e., to fix the ideas, located at more than one score of meters, with an apparatus 24x36 and a current optics), significant surface is in the focal plan; its distance with the principal plan H' image of the objective is then the focal distance. See also the article Not nodal .

A variation of the focal distance induced two concrete effects on the image seen through the objective:

“Growth of the object”

With the traditional format 24×36, for example, the focal distance known as " normale" , natural or average is approximately of 43 mm (it is the diagonal of the image 24×36 mm): with this focal distance, it is of use to say that the image is perceived through the objective according to the same field angle as the human vision.

- The vision is a system with variable mental focusing: angle of attention (reading, examination of a detail) on 1°; angle of observation on 60°; angle of perception on 180°.

Actually this assertion must be moderate on several plans. Indeed the human vision does not proceed in the same way only the recording of an image behind an objective of focal distance fixes given: the eye has a field of view of great clearness or angle of attention (reading, examination of a detail) about 1 to 5 degrees, i.e. the field which a long focal distance of approximately 500 mm would record. Beyond these 5 degrees, the eye perceives the fine details less better. The eye sweeps the field without stop, the visual impression thus results from the permanent comparison of various fields to which the eye turns. Nevertheless, one speaks about angle of observation, which covers approximately 60° in the horizontal plane. It is this angle which is used as reference for the focal distance " normale" for the format considered. In addition, the eye has a sensitivity to the movements and the light which reaches almost the 180°, that describes the angle of " perception".

Another important point it is the way in which the sights are regulated. For example it is current that the sights of the reflex cameras 24×36 are regulated so that the focal distance of 35 mm gives a optical Grossissement identical so that the naked eye would see; the 50 mm is thus affected, through the sight of these apparatuses, of a factor of enlargement of 50/35 = 1,4.

In the apparatuses not rangefinder reflex camera, according to the model, the sight can be built or regulated with various values of enlargement between 0,5 and 1,25 (with a front lens); thanks to framework-reference marks in the sight, which is seen in the sight is connected with what the objectives of various focal distances will record on the surface of 24×36 Misters.

It is clear that the sights taken with the very great angles or the very long focal distances have something of “non-naturel”, it is thus legitimate to seek to place between the two a normal or natural focal distance. The concept of “normal focal distance” covering an angle of 53° (diagonal = focal), without excluding completely from the reasons of physiological optics, perhaps undoubtedly must more with the history of the photographic technique. One can indeed evoke the historical weight of optics of the triplet type and tessar which covers, precisely, this angle with a good quality of images for an obstruction and reduced prices, formulas optical which dominated the market during almost a century.

Below, the same object photographed through various focal distances since the same point (the photographer does not move)

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