System Matrix: Two Thin Lenses
The position of the image formed by a pair of thin lenses can be found by the matrix method. The general matrix method involves multiplying a vector form of the incident vergence successively by matrices representing (1)the refraction by the first lens, (2) the translation to the second lens, and (3) the refraction by the second lens. If the system matrix is calculated, it can be used to directly multiply the incident vergence to obtain the exit vergence. From that exit vergence the image distance is calculated.
This example is for a two thin lenses surrounded by air (n=1). It involves the powers of the lens and the separation d of the lenses. It also involves the principal planes H1 and H2. As with most ordinary geometrical optics, it is applicable only for small angles (paraxial rays). The development also follows the cartesian sign convention.
A default set of values for the parameters of this calculation is provided. You can see the default calculation by entering a 0 into one of the lens parameters, which will trigger the entry of the default parameters for the lenses. Any of them may be then changed to explore the behavior of the lens system.
Note that the calculation does not take into account the change in lens separation with the angle of the incoming ray. It is typical to do the calculation only for the paraxial rays where the departure from full separation is negligible.
Thick lens concepts