How many stars of sixth-magnitude would it take for a small cluster to appear as bright as a single first-magnitude star? A) 10⁵ B) 5 C) 6 D) 100

Question

Quizplus · Accepted Answer

The magnitude scale is logarithmic, with a difference of 5 magnitudes corresponding to a brightness factor of 100. Therefore, each step in magnitude changes the brightness by a factor of about 2.512 (the fifth root of 100). A difference of 5 magnitudes (from first to sixth) means a single first-magnitude star is 100 times brighter than a sixth-magnitude star, requiring 100 sixth-magnitude stars to match its brightness.

How Many Stars of Sixth-Magnitude Would It Take for a Small