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 $5000\stackrel{\circ }{A}$, is of the order of

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

Answer 1

The correct option is C 5 mm

Suppose minimum distance between objects is x and their distance from telescope is r
So Resolving $limi{t}^{d\theta =\frac{1.22\lambda }{a}=\frac{x}{r}}\Rightarrow x=\frac{1.22\lambda \times r}{a}=\frac{1.22\times (5000\times {10}^{-10})\times (1\times {10}^3)}{\left(0.1\right)}=6.1\times {10}^{-3}m=6.1mm$
Hence, It’s order is $\approx 5mm$.