The focal length of the objective lens of a telescope is 50 cm. If the

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The focal length of the objective lens of a telescope is 50 cm. If the magnification of the telescope is 25, then the focal length of the eye-piece is

12.5 cm
5 cm
2 cm
10 cm
This question was previously asked in
UPSC NDA-1 – 2019
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The focal length of the eye-piece is 2 cm.
For a refracting telescope used in normal adjustment (final image at infinity), the angular magnification (M) is given by the ratio of the focal length of the objective lens (f_o) to the focal length of the eye-piece lens (f_e): M = f_o / f_e.
Given f_o = 50 cm and M = 25.
We can rearrange the formula to solve for f_e: f_e = f_o / M.
Substituting the given values: f_e = 50 cm / 25 = 2 cm.
A telescope achieves magnification by using an objective lens with a long focal length and an eye-piece lens with a short focal length. The objective forms a real, inverted image of a distant object at its focal plane, and the eye-piece acts as a magnifying glass to view this intermediate image.

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