Two point sources of light of wavelength 600 nm are being viewed by a telescope of aperture width 2.0 cm.What is the closest angular separation at which the two sources can be resolved? A) 7.3 $\times$ 10^-5 rad B) 3.7 $\times$ 10^-5 rad C) 7.3 $\times$ 10^-5 deg D) 3.7 $\times$ 10^-5 deg E) 4.2 $\times$ 10^-3 deg

Question

Quizplus · Accepted Answer

The angular resolution of a telescope can be approximated by the Rayleigh criterion, which is given by:
θ = 1.22λ/D
where θ is the minimum angular separation that can be resolved, λ is the wavelength of light, and D is the diameter of the aperture of the telescope.
Substituting the given values, we get:
θ = 1.22(600 nm)/(2.0 cm)
θ = 3.7 x 10^-5 radians
Converting to degrees, we get:
θ = 2.1 x 10^-3 degrees
Therefore, the closest angular separation at which the two sources can be resolved is approximately 3.7 x 10^-5 radians or 2.1 x 10^-3 degrees, which is closest to option B.

Two Point Sources of Light of Wavelength 600 Nm Are ×\times×

Two Point Sources of Light of Wavelength 600 Nm Are $\times$