Focal length

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. A positive focal length indicates that a system converges light, while a negative focal lengh indicates that the system diverges light. 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. 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. For more general optical systems, the focal length has no intuitive meaning; it is simply the inverse of the system's optical power. 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. A positive focal length indicates that a system converges light, while a negative focal lengh indicates that the system diverges light. 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. 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. For more general optical systems, the focal length has no intuitive meaning; it is simply the inverse of the system's optical power. 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. 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. 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. 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 considered that point at which the spreading beams of light would meet before the lens if the lens were not there. No image is formed during such a test, and the focal length must be determined by passing light (for example, the light of a lase 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. For a thick lens (one which has a non-negligible thickness), or an imaging system consisting of several lenses 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: For an optical system in air, the effective focal length (f and f′) gives the distance from the front and rear principal planes (H and H′) to the corresponding focal points (F and F′). If the surrounding medium is not air, then the distance is multiplied by the refractive index of the medium (n is the refractive index of the substance from which the lens itself is made; n1 is the refractive index of any medium in front of the lens; n2 is that of any medium in back of it). Some authors call these distances the front/rear focal lengths, distinguishing them from the front/rear focal distances, defined above. 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.