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A telescope of aperture $3 \times 10^{-2} \mathrm{~m}$ diameter is focused on a window at $80 \mathrm{~m}$ distance fitted with a wire mesh of spacing $2 \times 10^{-3} \mathrm{~m}$. Given: $\lambda=5.5 \times 10^{-7} \mathrm{~m}$, which of the following is true for observing the mesh through the telescope?
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The correct answer is:
Yes, it is possible with the same aperture size.
Yes, it is possible with the same aperture size.
Given : $d=3 \times 10^{-2} \mathrm{~m}$
$$
\lambda=5.5 \times 10^{-7} \mathrm{~m}
$$
Limit of resolution, $\Delta \theta=\frac{1.22 \lambda}{d}$
$$
=\frac{1.22 \times 5.5 \times 10^{-7}}{3 \times 10^{-2}}=2.23 \times 10^{-5} \mathrm{rad}
$$
At a distance of $80 \mathrm{~m}$, the telescope is able to resolve between two points which are separated by $2.23 \times 10^{-5} \times 80 \mathrm{~m}$ $=1.78 \times 10^{-3} \mathrm{~m}$
$$
\lambda=5.5 \times 10^{-7} \mathrm{~m}
$$
Limit of resolution, $\Delta \theta=\frac{1.22 \lambda}{d}$
$$
=\frac{1.22 \times 5.5 \times 10^{-7}}{3 \times 10^{-2}}=2.23 \times 10^{-5} \mathrm{rad}
$$
At a distance of $80 \mathrm{~m}$, the telescope is able to resolve between two points which are separated by $2.23 \times 10^{-5} \times 80 \mathrm{~m}$ $=1.78 \times 10^{-3} \mathrm{~m}$
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