Focal length
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The focal length of an
In most
Thin lens approximation
For a thin lens in air, the focal length is the distance from the center of the
When a lens is used to form an image of some object, the distance from the object to the lens u, the distance from the lens to the image v, and the focal length f are related by
The focal length of a thin convex lens can be easily measured by using it to form an image of a distant light source on a screen. The lens is moved until a sharp image is formed on the screen. In this case 1/u is negligible, and the focal length is then given by
Determining the focal length of a concave lens is somewhat more difficult. The focal length of such a lens is defined as the point at which the spreading beams of light meet when they are extended backwards. No image is formed during such a test, and the focal length must be determined by passing light (for example, the light of a laser beam) through the lens, examining how much that light becomes dispersed/ bent, and following the beam of light backwards to the lens's focal point.
General optical systems
For a thick lens (one which has a non-negligible thickness), or an imaging system consisting of several lenses or mirrors (e.g. a
- Effective focal length (EFL)
- The effective focal length (previously equivalent focal length but not to be confused with nodal pointswithout tracing any rays.
- Front focal length (FFL)
- The front focal length f is the distance from the front focal point F to the front principal planeH.
- Rear focal length (RFL)
- The rear focal length f' is the distance from the rear principal plane H' to the rear focal point F'.
- Front focal distance (FFD)
- The front focal distance (FFD) (sF) is the distance from the front focal point of the system (F) to the Some authors refer to this as "front focal length".
- Back focal distance (BFD)
- Back focal distance (BFD) (s′F′) is the distance from the vertex of the last optical surface of the system (S2) to the rear focal point (F′).[1][3] Some authors refer to this as "back focal length".
For an optical system in air the effective focal length, front focal length, and rear focal length are all the same and may be called simply "focal length".
For an optical system in a medium other than air or vacuum, the front and rear focal lengths are equal to the EFL times the refractive index of the medium in front of or behind the lens (n1 and n2 in the diagram above). The term "focal length" by itself is ambiguous in this case. The historical usage was to define the "focal length" as the EFL times the index of refraction of the medium.[2][4] For a system with different media on both sides, such as the human eye, the front and rear focal lengths are not equal to one another, and convention may dictate which one is called "the focal length" of the system. Some modern authors avoid this ambiguity by instead defining "focal length" to be a synonym for EFL.[1]
The distinction between front/rear focal length and EFL is important for studying the human eye. The eye can be represented by an equivalent thin lens at an air/fluid boundary with front and rear focal lengths equal to those of the eye, or it can be represented by a different equivalent thin lens that is totally in air, with focal length equal to the eye's EFL.
For the case of a lens of thickness d in air (n1 = n2 = 1), and surfaces with
where n is the refractive index of the lens medium. The quantity 1/f is also known as the optical power of the lens.
The corresponding front focal distance is:[5]
and the back focal distance:
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 negative if the second surface is convex, and positive if concave. Sign conventions vary between different authors, which results in different forms of these equations depending on the convention used.
For a
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
Camera lens focal lengths are usually specified in millimetres (mm), but some older lenses are marked in centimetres (cm) or inches.
Focal length (f) and field of view (FOV) of a lens are inversely proportional. For a standard rectilinear lens, FOV = 2 arctan x/2f, where x is the width of the film.
When a photographic lens is set to "infinity", its rear
To render closer objects in sharp focus, the lens must be adjusted to increase the distance between the rear principal plane and the film, to put the film at the image plane. The focal length (f), the distance from the front principal plane to the object to photograph (s1), and the distance from the rear principal plane to the image plane (s2) are then related by:
As s1 is decreased, s2 must be increased. For example, consider a
The focal length of a lens determines the magnification at which it images distant objects. It is equal to the distance between the image plane and a
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;[8] this angle of view is about 53 degrees diagonally. For full-frame 35 mm-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 35 mm-format cameras), while a lens significantly longer than normal may be referred to as a telephoto lens (typically 85 mm and more, for 35 mm-format cameras). Technically, long focal length lenses are only "telephoto" if the focal length is longer than the physical length of the lens, but the term is often used to describe any long focal length lens.
Due to the popularity of the
Optical power
The
The main benefit of using optical power rather than focal length is that the
See also
- Depth of field
- Dioptre
- f-number or focal ratio
References
- ^ a b c d ,
John E. Greivenkamp (2004). Field Guide to Geometrical Optics. ISBN 978-0-8194-5294-8.
- ^ a b Simpson MJ. Focal Length, EFL, and the Eye. Applied Optics, v62, n7, 1 March 2023 p1853-1857. https://doi.org/10.1364/AO.481805
- ^ ISBN 978-0805385663.
- ^ Simpson MJ, "Nodal points and the eye", Appl. Opt. 61, 2797-2804 (2022) https://doi.org/10.1364/AO.455464
- ISBN 978-0805385663.
- ^
Charles, Jeffrey (2000). Practical astrophotography. Springer. pp. 63–66. ISBN 978-1-85233-023-1.
- ^
Stroebel, Leslie; Zakia, Richard D. (1993). The Focal encyclopedia of photography (3rd ed.). ISBN 978-0-240-51417-8.
- ^
Stroebel, Leslie D. (1999). View Camera Technique. ISBN 978-0-240-80345-6.
- ISBN 0-8194-5294-7.