Question

What is the minimum angular separation between two stars if a telescope is used to observe them with an objective of circular aperture $20cm$? The wavelength light used is $5900\stackrel{\text{0}}{\text{A}}.$

• A. $4\times {10}^{-6}rad$
• B. $3.6\times {10}^{-6}rad$
• C. $2\times {10}^{-6}rad$
• D. $5\times {10}^{-6}rad$

Answer 1

The correct option is B $3.6\times {10}^{-6}rad$

Aperture:

$A=20$cm$=0.2$m

Wavelength:

$\lambda =5900$A$=5.9\times {10}^{-7}$m

Minimum angular seperation:

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

$=\frac{1.22\times 5.9\times {10}^{-7}}{0.2}$

$=3.6\times {10}^{-6}$rad