focal length

A telescope's focal length is the distance that light travels from the primary lens or mirror to the focal plane (or if there is a secondary lens or mirror, where the focal plane would be if the secondary were removed). The reciprocal of the focal length is the optical power (i.e., the kind of power specified for binoculars or small telescopes).

The focal ratio (aka F-ratio, or for cameras, the F-stop or F-number) is the ratio of the focal length to the diameter of the aperture. For cameras, the focal ratio is important for determining the depth of field. For telescopes, it is important for determining the field of view (FOV): other elements being the same, the smaller the focal ratio, the larger the FOV, and telescopes aiming at surveys often are given short focal ratios (e.g., Schmidt cameras).

The lensmaker's formula (or lensmaker's equation) allows calculation of the focal length of a lens:

1/f ≈ (n-1)(1/R1+1/R2)

• f - focal length
• n - refractive index of the lens material (a fractional measure showing how much it affects light's speed).
• R₁, R₂ - the radii of curvature of the two sides of the lens.

A more accurate version, significant if the lens is not thin:

1/f = (n-1)(1/R1+1/R2+(n-1)d/(nR1R2))

• d - thickness of the lens, through the center, specifically where the lens surfaces are perpendicular to a line straight through.

For a paraboloid mirror described by z=Ar², (r=radius, from the optical axis), the focal length is 1/(4A), which is the distance from the paraboloid's vertex to its focal point. A spherical mirror's focal length is half the sphere's radius. Spherical mirrors and other (non-paraboloid) circularly-symmetric curved mirrors approximate a paraboloid's curvature near their vertex, and their focal length is essentially that of the paraboloid that they approximate.