Question

A telescope of objective lens diameter $2m$ uses light of wavelength $5000\mathring{A}$ for viewing starts. The minimum angular separation between two stars whose image is just resolved by their telescope is:

• A. $4\times {10}^{-4}rad$
• B. $40.25times{10}^{-6}rad$
• C. $0.31\times {10}^{-6}rad$
• D. $5\times {10}^{-3}rad$

Answer 1

The correct option is C $0.31\times {10}^{-6}rad$

Given that,

Diameter $d=2m$

Wave length $\lambda =5000\stackrel{\circ }{A}$

Now, minimum angular separation is

$\Delta \theta =\frac{1.22\lambda }{d}$

$\Delta \theta =\frac{1.22\times 5000\times {10}^{-10}}{2}$

$\Delta \theta =0.3\times {10}^{-6}rad$

Hence, the resolving power is $0.3\times {10}^{-6}rad$