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 mean wavelength of light is $5000\dot{A}$, is of the order of :

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

Answer 1

The correct option is B 5 mm

We know,

Resolving Power = $\theta =\frac{d}{D}$ but $\theta \approx \frac{\lambda }{a}$

$(Note:exactrelation,\theta =\frac{1.22}{a}\lambda )$

$\frac{d}{D}=\frac{\lambda }{a}\Rightarrow =d=\frac{\lambda D}{a}$

$\Rightarrow d=\frac{5000\times {10}^{-10}\times {10}^3}{10\times {10}^{-2}}=5mm$