A telescope has an objective lens of 10 $\mathrm{cm}$ diameter and is situated at a distance of one kilometers from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is $5000 Å$, is of the order of:

• A

  $0.5 \mathrm{~m}$
• B

  $5 \mathrm{~m}$
• Correct answer
  C

  $5 \mathrm{~mm}$
• D

  $5 \mathrm{~cm}$

Solution

According to the question: $\begin{array}{ll} \theta =\frac{1.22}{a} \lambda \\ \therefore \frac{d}{D} =\frac{\lambda}{\mathrm{a}} \\ \Rightarrow a^{\prime}=\frac{\lambda D}{a} \\ a =\frac{5000 \times 10^{-10} \times 10^3}{10 \times 10^{-2}}=5 \mathrm{~mm} \end{array}$

Hence, the correct answer is option: 'C'.