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