Question

A telescope has an objective lens of $10 \,cm$ diameter and is situated at a distance of 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, $\mathring{A}$ is of the order of

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

Answer 1

Answer: (C)

5 mm

Answer 2

$\theta = \frac{d}{D}$ but $\theta \approx \frac{\lambda}{a}$ (Note : $-$ exact relation $\theta=\frac{1.22}{ a } \lambda$ ) $\frac{ d }{ D }=\frac{\lambda}{ a } \Rightarrow d =\frac{\lambda D }{ a }$ $\Rightarrow d =\frac{5000 \times 10^{-10} \times 10^{3}}{10 \times 10^{-2}}=5 \,mm$