Focal Length - General Optical Systems

General Optical Systems

For a thick lens (one which has a non-negligible thickness), or an imaging system consisting of several lenses and/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:

• Front focal length (FFL) or Front focal distance (FFD) is the distance from the front focal point of the system to the vertex of the first optical surface.
• Back focal length (BFL) or Back focal distance (BFD) is the distance from the vertex of the last optical surface of the system to the rear focal point.

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.

For the case of a lens of thickness d in air, and surfaces with radii of curvature R₁ and R₂, the effective focal length f is given by:

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:

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 positive if the second surface is concave, and negative if convex. Note that sign conventions vary between different authors, which results in different forms of these equations depending on the convention used.

For a spherically curved mirror in air, the magnitude of the focal length is equal to the radius of curvature of the mirror divided by two. The focal length is positive for a concave mirror, and negative for a convex mirror. In the sign convention used in optical design, a concave mirror has negative radius of curvature, so

,

where 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.