In general, the angle of view depends also on the distortion. This model leads to the simple geometric model that photographers use for computing the angle of view of a camera in this case, the angle of view depends only on the ratio of focal length to film size. For rectilinear lenses (that is, with no image distortion), the imaging of distant objects is well modelled as a pinhole camera model. It is equal to the distance between the image plane and a pinhole that images distant objects the same size as the lens in question. The focal length of a lens determines the magnification at which it images distant objects. To focus an object 1 m away ( s 1 = 1,000 mm), the lens must be moved 2.6 mm farther away from the image plane, to s 2 = 52.6 mm. To focus a distant object ( s 1 ≈ ∞), the rear nodal point of the lens must be located a distance s 2 = 50 mm from the image plane. For example, consider a normal lens for a 35 mm camera with a focal length of f = 50 mm. Īs s 1 is decreased, s 2 must be increased. 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 byġ f = 1 u + 1 v. 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. 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. On the other hand, in applications such as microscopy in which magnification is achieved by bringing the object close to the lens, a shorter focal length (higher optical power) leads to higher magnification because the subject can be brought closer to the center of projection.įor 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 most photography and all telescopy, where the subject is essentially infinitely far away, longer focal length (lower optical power) leads to higher magnification and a narrower angle of view conversely, shorter focal length or higher optical power is associated with lower magnification and a wider angle of view. For more general optical systems, the focal length has no intuitive meaning it is simply the inverse of the system's optical power. For the special case of a thin lens in air, a positive focal length is the distance over which initially collimated (parallel) rays are brought to a focus, or alternatively a negative focal length indicates how far in front of the lens a point source must be located to form a collimated beam.
A system with a shorter focal length bends the rays more sharply, bringing them to a focus in a shorter distance or diverging them more quickly. A positive focal length indicates that a system converges light, while a negative focal length indicates that the system diverges light. The focal length of an optical system is a measure of how strongly the system converges or diverges light it is the inverse of the system's optical power.
The focal point F and focal length f of a positive (convex) lens, a negative (concave) lens, a concave mirror, and a convex mirror.