The Hubble Space Telescope has excellent resolving power becausethere is no atmo

Question

The Hubble Space Telescope has excellent resolving power becausethere is no atmospheric distortion of the light. The Hubble deepfield camera uses the 2.4-m-diameter mirror to collect light
from distant galaxies that formed very early in the history of theuniverse. How far apart can two galaxies be from each other if theyare 10 billion light-years away from Earth and are barely resolvedby the Hubble Telescope using visible light with a wavelength of400 nm?

(A) 2.0×103 ly (B) 2.9×103 ly (C) 3.1×103ly (D) 4.0×103 ly (E) 4.2×103 ly

Explanation / Answer

We know , resolving power of a telescope =1.22/D where D= diameter =2.4 m So resolving power =2.03*10-7 Resolving power = sin . so for small angle of , so for small angle of , Sin= L/L Where L is the distance between two objects L= distance from telescope. Here L=L*2.03*10-7 L=2.03*103 light year

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