All Problems Photometry and Geometrical Optics
Problem 5.56
An aligned optical system consists of two thin lenses with focal lengths \(f_{1}\) and \(f_{2}\), the distance between the lenses being equal to \(d\). The given system has to be replaced by one thin lens which, at any position of an object, would provide the same transverse magnification as the system. What must the focal length of this lens be equal to and in what position must it be placed with respect to the two-lens system?
5.56. \(f=\frac{f_{1} f_{2}}{f_{1}+f_{2}-d}\). The lens should be positioned in the front principal plane of the system, i.e. at a distance of \(x=\) \(=f_{1} d \bar{l}\left(f_{1}+f_{2}-d\right)\) from the first lens.