A telescope has an aperture of 20.3 cm.How far apart must two blue stars (wavelength = 490 nm)be if they are 65 light years away (1 ly = 9.46 * 10¹⁵m)in order for the telescope to be able to resolve the two stars?

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Quizplus · Accepted Answer

The Rayleigh criterion states that two objects are just resolvable when the center of the diffraction pattern of one object is directly over the first minimum of the diffraction pattern of the other object. The angular resolution of a telescope is given by:$$ heta = 1.22 \frac{\lambda}{D}$$where $ heta$ is the angular resolution, $\lambda$ is the wavelength of light, and D is the diameter of the telescope's aperture.The distance between two stars is given by:$$d = heta L$$where d is the distance between the stars, $ heta$ is the angular resolution, and L is the distance to the stars.Substituting the given values into the equations, we get:$$ heta = 1.22 \frac{490 imes 10^{-9} ext{ m}}{0.203 ext{ m}} = 2.95 imes 10^{-6} ext{ rad}$$$$d = (2.95 imes 10^{-6} ext{ rad})(65 ext{ ly})(9.46 imes 10^{15} ext{ m/ly}) = 1.81 imes 10^{12} ext{ m}$$Therefore, the two stars must be 1.81 * 10¹²m apart in order for the telescope to be able to resolve them.

A Telescope Has an Aperture of 20