If the tube length of an astronomical telescope is 96 cm and its magnifying power is 15 for normal setting, then the focal length of the objective is cm.

Question

Accepted Answer

(2) 90. Given: normal adjustment, tube length L = fₒ+fₑ = 96 cm, magnifying power m = (fₒ)/(fₑ) = 15. Idea: in normal adjustment the final image is at infinity, so the objective's focal point and the eyepiece's focal point coincide and the tube is just fₒ+fₑ. Two equations, two unknowns: write fₒ = 15fₑ and substitute. 15fₑ+fₑ = 96, so 16fₑ = 96 and fₑ = 6 cm. Then fₒ = 15× 6 = 90 cm. Check: 90+6 = 96 cm and (90)/6 = 15, so the objective's focal length is 90 cm.

If the tube length of an astronomical telescope is 96 cm and its magnifying power is 15 for normal setting, then the focal length of the objective is ______ cm.

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