Question

The diameter of an objective of a telescope, which can just resolve two stars situated at an angular displacement of ${10}^{-4}$ degree, should be $\left(\lambda =5000A^0\right)$

• A. 35 mm
• B. 35 cm
• C. 35 m
• D. None of the above

Answer 1

The correct option is B 35 cm

$\Delta \theta =\left(\frac{1.22\lambda }{d}\right)$
$d=\left(\frac{1.22\times \lambda }{\Delta \theta }\right)$
$\Rightarrow {10}^{-4}\to \frac{\lambda }{180}\times {10}^{-4}$
$=1.74\times {10}^{-6}rad.$
$d=\left(\frac{1.22\times 5000\times {10}^{-10}}{1.74\times {10}^{-6}}\right)$
$=0.35mor35cm$