Afocal systems, magnification

In formula (37), we notice that in cases where distance e between two lenses is equal to f '1 + f '2 , f ' is infinite, Cv is null. The point at infinity is the image to itself. The system has no focus. The image focus of the first lens is confounded with the object focus of the second.

In the case of a complex system S in the air composed of two sub systems, as soon as the image focus of the first is confounded with the object focus of the second, the system is afocal.

Such is the case for visual observation systems as glasses, binoculars, telescopes.

The above figure shows such a system, composed of two sub systems which are assimilated to thin lenses L1 and L2. Object B is to infinity in the direction θ. The main properties found in these afocal systems are :

• F'1 confounded with F2

• The object point at infinity is the image to itself.

• Transversal magnification is constant :

• Angular magnification G is constant :

An astronomical telescope is an afocal instrument composed of a head system called the objective which gives an intermediate image. This image is observed with an ocular which, from the intermediate image, gives an image situated at infinity observable by the eye. The magnification is negative, images are inverted.

The terrestrial visual afocal instruments (glasses, binoculars) have a reversing device, generally with prisms, between the lens and the ocular, which gives a positive enlarging.

In a binoculars body, a set of two Porro's prisms enables a 180° rotation of the image around the optical axis and thereby straightens the images.

Galilee's binoculars: It is characterized by a second divergent system, the magnification is then positive, the images are straight but the field is much reduced. We use them with weak magnification such as theatre binoculars.