Association of two optical systems

Let an optical system S be made of two sub systems S1 (F1F'1H1H'1) and S2 (F2F'2H2H'2) with a focal distance f '1 et f ' 2. Let us look for the optical properties of S.

The entrance index is n, the intermediate index N, the exist index n'.

An object to infinity AB with angular dimension θ yields, in the image focal plane F'1B'1 of S1, an image with a dimension y'1 = -f1.θ following (28). The systemS2 renders a definitive image F'B' in the image focal plane of S of which the dimension y' can be expressed by :

The magnification gy2 of the conjugation F'1→F' :

y' = y'1 .gy2 = -f1.θ.gy2

The relationship (28) applied to S, f being the object focal distance of S :

y' = - f.θ

We deduct the object focal distance of S :

Gullstrand's formula give a simple relationship beween the convergences Cv, Cv1, Cv2 de S, S1, S2, distance and the intermediate index N :