Chapter 33, Problem 108GP

A telephoto lens system obtains a large magnification in a compact package. A simple such system can be constructed out of two lenses, one converging and one diverging, of focal lengths f₁ and $f_2=-\frac{1}{2}f$, respectively, separated by a distance $\mathcal{l}=\frac{3}{4}{f}_1$ as shown in Fig. 33–51. (a) For a distant object located at distance d_o from the first lens, show that the first lens forms an image with magnification m₁ ≈ −f₁/d_o located very close to its focal point. Go on to show that the total magnification for the two-lens system is m ≈ −2f₁/d_o. (b) For an object located at infinity, show that the two-lens system forms an image that is a distance $\frac{3}{4}{f}_1$ behind the first lens. (c) A single 250-mm-focal-length lens would have to be mounted about 250 mm from a camera’s film in order to produce an image of a distant object at d_o with magnification −(250 mm)/d_o. To produce an image of this object with the same magnification using the two-lens system, what value of f₁ should be used and how far in front of the film should the first lens be placed? How much smaller is the “focusing length” (i.e., first lens-to-final image distance) of this two-lens system in comparison with the 250-mm “focusing length” of the equivalent single lens?

FIGURE 33–51 Problem 108.