Optical Instruments — Question 8

Question 8

Telescope length and angular magnification determine both focal lengths

An astronomical telescope has two converging thin lenses and is adjusted for relaxed viewing. Its lens separation is 84 cm and its signed angular magnification is -20. The objective diameter is 40 mm.

1. Find the objective and eyepiece focal lengths.

2. Find the exit-pupil diameter using the eyepiece image of the objective, or the equivalent ratio $D_{\mathrm{exit}}=D_o f_e/f_o$.

Question 8 - Solution

Telescope length and angular magnification determine both focal lengths

(a) Method and calculation

$$d=f_o+f_e=84\,\mathrm{cm},\quad M=-f_o/f_e=-20.$$$$f_o=20f_e\Rightarrow\boxed{f_e=4\,\mathrm{cm},\quad f_o=80\,\mathrm{cm}}.$$

(b) Interpretation and further calculation

$$\boxed{D_{\mathrm{exit}}=40(4/80)=2.0\,\mathrm{mm}}.$$$$\boxed{|M|D_{\mathrm{exit}}=D_o=40\,\mathrm{mm}}.$$

Physical check

The exit pupil is an image of the objective aperture, not an image of the distant scene.