Chapter 3.3, Problem 20E

Focal Length A refracting telescope has a main lens, or objective lens, and a second lens, the eyepiece (see Figure 3.42). For a given magnification $M$ of the telescope, the focal length $F_{°}$ of the objective lens is a linear function of the focal length $F_e$ of the eyepiece. For example, a telescope with magnification $M=80$ times can be constructed using various combinations of lenses. The following table gives some samples of focal length for telescopes with magnification $M=80$. Here focal lengths are in centimeters.

$F_e$	$0.3$	$0.5$	$0.7$	$0.9$
$F_{°}$	$24$	$40$	$56$	$72$

a. Construct a linear model for the data.

b. In this example, the magnification $M$ is 80. In general, $F_{°}$ is proportional to $F_e$, and the constant of proportionality is $M$. Use this relation to write a formula for $F_{°}$ in terms of $F_e$ and $M$.

c. Solve the equation you obtained in part b for $M$ and thus obtain a formula for magnification as a function of objective lens focal length and eyepiece focal length.

d. To achieve a large magnification, how should the objective and eyepiece lenses be selected?

FIGURE 3.42