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