Two stars in Earth's sky have the same apparent brightness. If neither of them is hidden behind gas or dust clouds, then one knows that they
A) must be at the same distance from Earth.
B) may be at different distances, in which case the nearer one must have the greater luminosity.
C) may be at different distances, in which case the farther one must have the greater luminosity.
D) must have the same temperature.

Question

Quizplus · Accepted Answer

Two stars appearing with the same apparent brightness can indeed be at different distances from Earth. If they are at different distances, the farther one must have a greater intrinsic luminosity (actual brightness) to appear as bright as the nearer one. This is because the apparent brightness of a star decreases with the square of the distance from the observer, according to the inverse square law of light.

Two Stars in Earth's Sky Have the Same Apparent Brightness