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An astronomical telescope has a length of 44 cm and tenfold magnification. The focal length of the objective lens is

1. 4 cm
2. 40 cm
3. 44 cm
4. 440 cm

Correct answer: 40 cm

Solution

The length of an astronomical telescope is given by the sum of the focal lengths of the objective and eyepiece lenses. For a magnification of 10, the focal length of the objective lens is 10 times that of the eyepiece. Let the focal length of the eyepiece be f_e. Then, f_o = 10f_e. From the length equation, f_o + f_e = 44 cm. Substituting f_o = 10f_e, we get 10f_e + f_e = 44, or 11f_e = 44, so f_e = 4 cm and f_o = 40 cm.

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