Aperture - focal length

Lenses or mirrors of telescope are characterized by these two values :

The aperture - usually named D - is the diameter of the lens or the mirror. It is often the diameter of the optical element but it can be also the aperture limited by a diaphragm.

• The quantity of collected light varies according to the square of the aperture. With regard to the eye, having a "standard" aperture d of 6mm, an objective of opening D = 60mm receives: ( D/d) x ( D/d) = (10) x (10) = 100 times more light than the eye.

• The resolution is directly proportional to the aperture. With D in mm, we can quickly estimate it in arc-seconds by the formula :

  a = 120/D

The focal length (F) is the distance which separates the center of the objective and the point of convergence of beams resulting from an object very distant - a star is a good one. Typically, beam of sun light converges in a point which we named focus or in french "foyer", the place where is the fire. The distance focus-objective is the focal length F.

• The dimension of the image is directly proportional to the focal length. In the focal plan, an object of angular diameter "a" will have an image which dimension x is :

  x = 2.F.tg(α/2)       or       F.tg(α)   if α is very small   (α in rd)

• The luminosity of the image decreases according to the square of the focal length. (L prop. in 1/F ²)

Focal ratio : F/D

The previous elements thus show us that in theory, if we keep the same F/D ratio, the luminosity of the image remains unchanged.

Mirrors or lenses with a small F/D will be said more luminous than optics with high F/D. This indication also appears on the photographic objectives; we often speak then about values of diaphragm. The focal being fixed, we play on a diaphragm to change D and modify so the luminosity of the image. An objective with F/D = 2 is more luminous than has 5.6, etc....

Increasing focal length

It is possible to increase the image given by a telescope by means of a divergent lens, the famous Barlow lens. It allows to increase the focal of the objective and thus to operate a magnification of the image. In visual observation, Barlow lens is constituted by an achromatic doublet.

X = distance between Barlow lens and primary focus Fo.

T = distance between Barlow lens and new focus F1.

F = focal length of Barlow lens

Magnification:  G = (T/F) + 1      and       X = T/G