The Hale Telescope on Palomar Mountain in California has a mirror 200 in. (5.08

Question

The Hale Telescope on Palomar Mountain in California has a mirror 200 in. (5.08 m) in diameter and it focuses visible light. Given that a large sunspot is about 19, 400 ml in diameter, what is the most distant star on which this telescope could resolve a sunspot to see whether other stars have them? (Assume optimal viewing conditions, so that the resolution is diffraction limited. Assume that the visible wavelength ranges from 400 nm to 700 nm.) ___________________ km Are there any stars this close to us, besides our sun? Yes No

Explanation / Answer

Applying Rayleigh’s condition for the angular resolution of a circular aperture of diameter D>>:
= 1.22 /D
D = 5.08 m, d = 19400/0.621 = 31239.94 km
= 1.22 /D = s/z, provided s<<z,

where,
object distance:z
spatial separation between objects: s

z = s/ = s/(1.22 /D) = 31239.94x10³/(1.22*600x10^-9/5.08)

z = 2.2*10^8 km

There are no closer stars to earth besides the sun.
Alpha Centauri is 44x10^12 km away from earth and is the next closest star other than the sun.

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