Question

A telescope has an objective lens of 10 cm 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 wavelength of light is 5000AA, is of the order of

• A. 5 cm
• B. 0.5 m
• C. 5 mm
• D. 5 m

Hint:

Smaller wavelength and larger aperture improve resolving power.

Answer 1

The Correct Option is C

Step 1: Resolving power of telescope thetamin = 1.22(λ)/(D)
Step 2: Substituting values thetamin ≈ 1.22 × frac5×10⁻70.1 ≈ 6×10⁻6rad
Step 3: Linear separation x = Lθ = 1000 × 6×10⁻6 ≈ 6×10⁻3m ≈ 5mm