A telescope has an objective lens of 10 cm diameter and is situated...

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 telescope has an objective lens of 10 cm diameter and is situated at a distance of one kilometers from two objects.

Options

A $0.5 \mathrm{~m}$
B $5 \mathrm{~m}$
C $5 \mathrm{~mm}$
D $5 \mathrm{~cm}$

Correct answer

C. $5 \mathrm{~mm}$

Step-by-step solution

According to the question: A telescope has an objective lens of 10 cm diameter and is situated at a distance of one kilometers from two objects.

\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}

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