Question

ou are out stargazing with your 13.4-cm telescope. You point your telescope at an interesting formation in the sky, which you think is a binary star system. A binary star system consists of two stars in orbit around each other. You guess that the average wavelength coming from the stars is 518 nm. What is the minimum angular separation between the two stars required for your telescope to resolve the two stars of the binary system

Answer 1

θ = 4.716 10⁻⁶ rad

Step-by-step explanation:

In order for the releases to be considered separate, they must meet the Rayleigh criterion that establishes that the maximum diffraction of one star must coincide with the first minimum of the diffraction pattern of the second star.

We use the diffraction equation for a slit

a sin θ = m λ

The minimum occurs at m = 1

sin θ = λ / a

Since the angles in these systems are very small, we can approximate the sine to its angle in radians

θ = λ / a

The telescope has a circular aperture whereby polar cords should be used, which introduces a constant number

θ = 1.22 λ / a

Let's calculate

θ = 1.22 518 10⁻⁹ / 13.4 10⁻²

θ = 4.716 10⁻⁶ rad