If the tube length of an astronomical telescope is 105 cm and its magnifying power is 20 for normal setting, then the focal length of the objective is cm. (Hint: the optical length of an astronomical telescope is L = fₒ+fₑ.)

Question

Accepted Answer

(4) 100. Given: normal adjustment, so the tube length is L = fₒ+fₑ = 105 cm, with magnifying power m = (fₒ)/(fₑ) = 20. Idea: in normal adjustment the final image is at infinity, which puts the objective's focal point and the eyepiece's focal point at the same place; the tube is then just the sum of the two focal lengths. Substitute fₒ = 20fₑ into the length equation: 20fₑ+fₑ = 105. 21fₑ = 105, so fₑ = 5 cm. fₒ = 20× 5 = 100 cm. Check: 100+5 = 105 cm and (100)/5 = 20, so the objective's focal length is 100 cm.

If the tube length of an astronomical telescope is 105 cm and its magnifying power is 20 for normal setting, then the focal length of the objective is ______ cm. (Hint: the optical length of an astronomical telescope is L = fₒ+fₑ.)

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