Question

The angular resolution of telescope of 10 cm diameter at a wavelength of 5000 $A^{\circ }$ is of the order of :

• A. ${10}^{6}rad$
• B. ${10}^{-2}rad$
• C. ${10}^{-4}rad$
• D. ${10}^{-6}rad$

Answer 1

The correct option is D ${10}^{-6}rad$

Two point sources are regarded as just resolved when the principal diffraction maximum of one image coincides with the first minimum of the other.
If one considers diffraction through a circular aperture, this translates into the expression

$\theta =1.22\frac{\lambda }{d}=1.22\times \frac{5000\times {10}^{-8}}{10}=1.22\times 5\times {10}^{-6}=6\times {10}^{-6}rad$

Hence, the closest option is ${10}^{-6}rad$