Question

A telescope has an objective lens of 10cm diameter and is situated at a distance of one kilometer from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is 5000AA, is of the order of

• A. 6mm
• B. 6cm
• C. 6μm
• D. 6m

Hint:

Resolving power of a telescope improves with larger aperture and smaller wavelength: smin = (1.22λ L)/(D)

Answer 1

The Correct Option is A

Step 1: By Rayleigh criterion, angular resolution: θ = (1.22λ)/(D)

 Step 2: Linear separation: s = Lθ = (1.22λ L)/(D)

 Step 3: Substituting values: λ = 5000AA = 5×10⁻7m, L = 1000m, D = 0.1m s = frac1.22 × 5×10⁻7 × 10000.1 ≈ 6×10⁻3m s ≈ 6mm