A binary star system in the constellation Orion has an angular separation between the stars of 5*10^-5radians.Assuming a wavelength of 500 nm,what is the smallest aperture (diameter)telescope that will just resolve the two stars? (1 nm = 10^-9m) A)1 cm B)1.2 mm C)1.2 cm D)4 cm

Question

Quizplus · Accepted Answer

The smallest angular separation that can be resolved by a telescope is given by the Rayleigh criterion:
θ = 1.22 λ/D
where θ is the angular resolution, λ is the wavelength, and D is the diameter of the aperture.

In this case, we have:
θ = 5*10^-5 radians
λ = 500 nm = 5*10^-7 meters
We want to find D:
D = 1.22 λ/θ
D = 1.22 * 5*10^-7 / (5*10^-5)
D = 1.22*10^-2 meters = 1.22 cm

Therefore, the smallest aperture telescope that will just resolve the two stars is 1.2 cm, which corresponds to choice C.

A Binary Star System in the Constellation Orion Has an Angular