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What is the relationship between the focal length, f, of the objective and the resolving power of the telescope, R.P?

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What is the relationship between the focal length, f, of the objective and the resolving power of the telescope, R.P?

(a) f ∝ R.P

(b) f ∝ 1/R.P

(c) f^2 ∝ R.P

(d) no relation

This question was addressed to me during an internship interview.

The doubt is from Resolving Power topic in portion Optics of Engineering Physics II

1 Answer

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The correct answer is (b) f ∝ 1/R.P

Easiest explanation: For a telescope, the radius of the first dark ring = 1.22fλ/D

Therefore, the smaller will be the focal length of the objective, the sharper will be the diffraction pattern and hence the resolving power of the telescope would increase.

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