Question

10.42 We intend to observe two distant equal-brightness stars whose angular separation i 50.0 x 10 rad. Assuming a mean wavelength of 550 nm, what is the smallest-diameter objective lens that will resolve the stars (according to Rayleigh's criterion)?

Answer 1

For a Telescope to be able to resolve two nearby objects,

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

=> $d = 1.22\frac{\lambda}{\Delta \theta} = 1.22\frac{550\times 10^{-9}}{50\times 10^{-7}} = 0.1342 m = 13.42 cm$

this should be the smallest diameter of the objective lens which will resolve the stars.

2]

$\Delta \theta \approx tan\Delta \theta = \frac{x}{D}= 1.22\frac{\lambda}{d}$

x = 0.05 m

D = 161000 m

so, $\frac{0.05}{161000}= 1.22\frac{550\times 10^{-9}}{d}$

d = 2.1606 m

this is the diameter of the objective needed.