How does the resolving power of an astronomical telescope depend on the wavelength λ of light and the diameter D of its objective lens aperture?
Answer and explanation
Correct answer: B. Resolving power is directly proportional to D and inversely proportional to λ (RP ∝ D/λ)
- Step 1: By Rayleigh's criterion, the minimum angular separation (limit of resolution) between two point objects that can just be resolved by a circular telescope aperture of diameter is: .
- Step 2: The resolving power () of an optical instrument is defined as the reciprocal of its limit of resolution: .
- Step 3: Therefore: .
- Step 4: Thus, resolving power is directly proportional to the aperture diameter and inversely proportional to the wavelength .
Answer
Resolving power is directly proportional to D and inversely proportional to λ (RP ∝ D/λ)
Why not the others: 'RP ∝ λ/D' confuses resolving power with the limit of resolution ; 'Directly proportional to D²' confuses resolving power with light gathering power (which scales with area ); 'Inversely proportional to both' is mathematically incompatible with Rayleigh's formula.
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