A monochromatic light of wavelength $6000 Å$ coming from a star is detected in a 100 inch telescope. The…
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
$3.4 \times 10^{-7} \mathrm{rad}$
$6.7 \times 10^{-7} \mathrm{rad}$
$2.9 \times 10^{-7} \mathrm{rad}$
$1.54 \times 10^{-7} \mathrm{rad}$
Solution
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}
$