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A monochromatic light of wavelength $6000 Å$ coming from a star is detected in a 100 inch telescope. The limit of resolution of the telescope is approximately
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Verified Answer
The correct answer is:
$2.9 \times 10^{-7} \mathrm{rad}$
For a telescope, limit of resolution is given by
$$
Q_R=\frac{1.22 \lambda}{a}
$$
Here,
$$
\begin{aligned}
& \lambda=\text { wavelength of light }=600 Å \\
& a=\text { apperture size }=100 \text { inch } \\
& =100 \times 2.54 \mathrm{~cm}=254 \mathrm{~cm}
\end{aligned}
$$
So, Limit of resolution
$$
\begin{aligned}
Q_R & =\frac{1.22 \times 6000 \times 10^{-10}}{254 \times 10^{-2}}=28.8 \times 10^{-8} \mathrm{rad} \\
& =2.9 \times 10^{-7} \mathrm{rad}
\end{aligned}
$$
$$
Q_R=\frac{1.22 \lambda}{a}
$$
Here,
$$
\begin{aligned}
& \lambda=\text { wavelength of light }=600 Å \\
& a=\text { apperture size }=100 \text { inch } \\
& =100 \times 2.54 \mathrm{~cm}=254 \mathrm{~cm}
\end{aligned}
$$
So, Limit of resolution
$$
\begin{aligned}
Q_R & =\frac{1.22 \times 6000 \times 10^{-10}}{254 \times 10^{-2}}=28.8 \times 10^{-8} \mathrm{rad} \\
& =2.9 \times 10^{-7} \mathrm{rad}
\end{aligned}
$$
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