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With the help of a telescope that has an objective of diameter $200 \mathrm{~cm}$, it is proved that light of wavelengths of the order of $6400 Å$ coming from a star can be easily resolved. Then, the limit of resolution is
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The correct answer is:
$39 \times 10^8 \mathrm{rad}$
The limit of resolution of a telescope is
$$
\theta=\frac{1.22 \lambda}{d}
$$
where, $\lambda=$ wavelength of light rays
$d$ = aperture of objective lens of telescope.
Here, $\lambda=6400 Å=6400 \times 10^{-10} \mathrm{~m}$
$$
d=200 \mathrm{~cm}=2 \mathrm{~m}
$$
Substitution of values gives
$$
\begin{aligned}
\theta & =\frac{1.22 \times 6400 \times 10^{-10}}{2} \\
& =\frac{1.22 \times 64 \times 10^{-8}}{2} \\
& =1.22 \times 32 \times 10^{-8} \\
& =39 \times 10^{-8} \mathrm{rad}
\end{aligned}
$$
$$
\theta=\frac{1.22 \lambda}{d}
$$
where, $\lambda=$ wavelength of light rays
$d$ = aperture of objective lens of telescope.
Here, $\lambda=6400 Å=6400 \times 10^{-10} \mathrm{~m}$
$$
d=200 \mathrm{~cm}=2 \mathrm{~m}
$$
Substitution of values gives
$$
\begin{aligned}
\theta & =\frac{1.22 \times 6400 \times 10^{-10}}{2} \\
& =\frac{1.22 \times 64 \times 10^{-8}}{2} \\
& =1.22 \times 32 \times 10^{-8} \\
& =39 \times 10^{-8} \mathrm{rad}
\end{aligned}
$$
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