Two stars have the exact same luminosity, but star Y is four times dimmer looking that star X. This means that
A) star Y is four times as far away as star X
B) star Y is 16 times as far away as star X
C) star Y is half as far away as star X
D) star Y is twice as far away as star X
E) we can't figure out the relative distance of the two stars from the information given

Question

Quizplus · Accepted Answer

The brightness of a star depends on both its luminosity and its distance from us. If two stars have the exact same luminosity, but one appears four times dimmer than the other, we can conclude that the dimmer star must be four times farther away than the brighter star. This is because the apparent brightness of a star decreases with distance squared, so if we double the distance, the star's brightness decreases by a factor of four (2^2), and if we quadruple the distance, the brightness decreases by a factor of sixteen (4^2). Therefore, choice D is the best answer: star Y is twice as far away as star X.

Two Stars Have the Exact Same Luminosity, but Star Y