Question

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

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

Answer 1

Answer: (B)

5 m

Answer 2

Suppose minimum distance between objects is x and their distance from telescope is r

So Resolving limit $d\theta = \frac{1.22\lambda}{a} = \frac{x}{r}$

⇒$x = \frac{1.22\lambda \times r}{a} = \frac{1.22 \times (5000 \times 10^{- 10}) \times (1 \times 10^{3})}{(0 - 1)} = 6.1 \times 10^{- 3}m = 6.1mm$Hence, It’s order is ≈ 5 mm