Question

A telescope has an objective lens of $10cm$ 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 $5000\mathring{A},$ is of the order of

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

Answer 1

Answer: (D)

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