Problem 5.52

An optical system is located in air. Let \(O O^{\prime}\) be its optical axis, \(F\) and \(\hat{F}^{\prime}\) are the front and rear focal points, \(H\) and \(H^{\prime}\) are the front and rear principal planes, \(P\) and \(P^{\prime}\) are the conjugate points. By means of plotting find: (a) the positions \(F^{\prime}\) and \(H^{\prime}\) (Fig. \(5.11 a\) ); (b) the position of the point \(S^{\prime}\) conjugate to the point S (Fig. \(5.11 b)\) (c) the positions \(F, F^{\prime}\), and \(H^{\prime}\) (Fig. \(5.11 c\), where the path of the ray of light is shown before and after passing through the system).