Problem 5.34

By means of plotting find: (a) the path of a ray of light beyond thin converging and diverging lenses (Fig. 5.7 , where $O O^{\prime}$ is the optical axis, $F$ and $F^{\prime}$ are the front and rear focal points); (b) the position of a thin lens and its focal points if the position of the optical axis $O O^{\prime}$ and the positions of the cojugate points $P, P^{\prime}$ (see Fig. 5.5 ) are known; the media on both sides of the lenses are identical; (c) the path of ray 2 beyond the converging and diverging lenses (Fig. 5.8) if the path of ray 1 and the positions of the lens and of its optical axis $O O^{\prime}$ are all known; the media on both sides of the lenses are identical.