Question

A telescope can just resolve [Rayleigh Criterion] two objects which are 2000 km away from it. If separation between objects is 10 m and wavelength of light used is 500 nm then minimum diameter of objective of telescope is

• A. 12.2 cm
• B. 24.4 cm
• C. 30 cm
• D. 48.8 cm

Answer 1

The correct option is A 12.2 cm


$sin\theta =\frac{1.22\lambda }{D}$

Since $\theta$ is very small
$\theta =\frac{10}{2000\times {10}^3}$

$\frac{10}{2000\times {10}^3}=\frac{1.22\lambda }{D}\Rightarrow D=1.22\lambda \times 200\times {10}^3$
$\Rightarrow D=12.2cm$