Question

Question 12

The lens of a telescope has a diameter of 25 cm. You are using it to look at two stars that are 2 × 10¹⁷ m away from you and 6 × 10⁹ m from each other. You are measuring light with a wavelength of 700 nm. As the light goes through the lens, it diffracts.

a. Is it possible, using this telescope, to see the two stars as separate stars?

b. What is the minimum possible lens diameter you would need in order to resolve these two stars?

Answer 1

given
diameter of lens, d = 25 cm = 0.25 m
r = 2*10^17 m
s = 6*10^9 m
lamda = 700 nm = 700*10^-9 m

a) No. It is not possible.

angle subtended by the two stars at the lens, theta = s/r

= 6*10^9/(2*10^17)

= 3.0*10^-8 rad

minimum angular separation of two object to resolve them using telescope,

theta_min = 1.22*lamda/d

= 1.22*700*10^-9/0.25

= 3.416*10^-6 rad

clearly, theta < theta_min

so, it is not possible to see the two stars as separate stars.

b) let d_min is the minimum diameter of the lens to resolve the two stars.

use,

theta = 1.22*lamda/d_min

d_min = 1.22*lamda/theta

= 1.22*700*10^-9/(3*10^-8)

= 28.5 m <<<<<<<<----------------------Answer