The Hubble Space Telescope has detected galaxies with apparent magnitudes of about 30.Approximately how much fainter are these galaxies than stars with an apparent magnitude of 5? A) 10²⁵ times B) 10¹⁰ times C) 2,500 times D) 25 times

Question

Quizplus · Accepted Answer

The difference in brightness between two objects with apparent magnitudes m1 and m2 is given by the equation:
m2 - m1 = 2.5 log (F1/F2)
where F1 and F2 are the fluxes (amount of light) emitted by the objects.
If we assume that the galaxies detected by Hubble have an apparent magnitude of 30, and we want to compare them to stars with an apparent magnitude of 5, we can set m1 = 30 and m2 = 5 in the equation above:
5 - 30 = 2.5 log (Fgalaxies/Fstar)
-25 = 2.5 log (Fgalaxies/Fstar)
-25/2.5 = log (Fgalaxies/Fstar)
-10 = log (Fgalaxies/Fstar)
10^-10 = Fgalaxies/Fstar
This means that the flux emitted by the galaxies detected by Hubble is about 10 billion times fainter than the flux emitted by stars with an apparent magnitude of 5.
10 billion can be written as 10^1.1, which is approximately equal to 10^1. Therefore, the galaxies are about 10^1 or 10 times fainter than stars with an apparent magnitude of 5. Choice B is the closest option.

The Hubble Space Telescope Has Detected Galaxies with Apparent Magnitudes