Question

A telescope's objective diameter is 122 cm and light of 800 nm is used. If two stars at distance ${10}^8$ km are observed, what should be the minimum distance between them?

• A. 80 km
• B. 160 km
• C. 40 km
• D. 200 km

Answer 1

The correct option is A 80 km

$R.P=\frac{a}{1.22\lambda }$
= $\frac{122\times {10}^{-2}}{1.22\times 800\times {10}^{-9}}=\frac{1.22\times {10}^9}{1.22\times 800}=\frac{{10}^7}{8}$

$R.P=\frac{1}{{\theta }_{min}}$
$\Rightarrow {\theta }_{min}=8\times {10}^{-7}$


$\alpha =\frac{X}{D}>8\times {10}^{-7}$
X $>8\times {10}^{-7}\times {10}^8$
X $>80$ km