Exact formulas for a thin-lens system with an arbitrary number of lenses

We present an angular thin-lens formula giving the angle of refraction β for arbitrary values of the angle of incidence α. With this formula, we find analytical results for the focal length f of a thin-lens system. The number of lenses n and their focal lengths f1,f2,…,fn are abitrary, as are the mutual distances D12,…,D(n−1)n between the lenses. All these results are exact, i.e. not restricted to small or even paraxial angles. In the literature, the 2-lens and 3-lens versions (the last one without proof or derivation) are known [1]. We present the general result for n lenses and for (the positions of) its principal planes.