Image size, transversal magnification, angular magnification

Let us consider an object AB situated at a distance z from the diopter, with a radius, R in a plane perpendicular to the axis. Its image is A'B' at a distance z'. Let

In the paraxial approximation, as in figure 17 :

• A'B' is perpendicular to the axis

• θ is the object field angle, θ being small, tan(θ) = θ = y/z

• Similarly, θ' is the image field angle and θ' = y'/z'

• Refraction of the ray in S going from B is such that : nθ = n'θ'

We deduct the dimension y' of the image :

And the transversal growth gy :

For a given conjugation (AA') we define an angular growth between the angles relative to the axis of the two conjugated rays going through A and A'.

Following figure 17, I is the intersection of the rays with the diopter and the distance from I to the axis. In paraxial approximation, h is small, the diopter curvature is neglected and H is supposedly confounded with S. We have :

We thus deduct :

In cases where the object AB is to infinity, its transversal dimension is given by its field angle θ . Following figure 18, A is on the axis, its image is F', B', the image of B, is in the image focal plan at a distance y' from the axis in such a way that :