Question 33.15: Telescope magnification. The largest optical refracting tele......
Telescope magnification. The largest optical refracting telescope in the world is located at the Yerkes Observatory in Wisconsin, Fig. 33-37. It is referred to as a “40-inch” telescope, meaning that the diameter of the objective is 40 \,\mathrm{in}., or 102 \mathrm{~cm}. The objective lens has a focal length of 19 \mathrm{~m}, and the eyepiece has a focal length of 10 \mathrm{~cm}. (a) Calculate the total magnifying power of this telescope. (b) Estimate the length of the telescope.
APPROACH Equation 33-7 gives the magnification. The length of the telescope is the distance between the two lenses.
M=\frac{\theta^{\prime}}{\theta}=\frac{\left(h / f_{\mathrm{e}}\right)}{\left(h / f_{\mathrm{o}}\right)}=-\frac{f_{\mathrm{o}}}{f_{\mathrm{e}}}\qquad [telescope] (33-7)
(a) From Eq.33-7 we find
M=-\frac{f_{\mathrm{o}}}{f_{\mathrm{e}}}=-\frac{19 \mathrm{~m}}{0.10 \mathrm{~m}}=-190 \times
(b) For a relaxed eye, the image I_{1} is at the focal point of both the eyepiece and the objective lenses. The distance between the two lenses is thus f_{\mathrm{o}}+f_{\mathrm{e}} \approx 19 \mathrm{~m}, which is essentially the length of the telescope.