Final answer:
Two stars with identical luminosities can differ in apparent brightness due to their distances from the observer; the closer star will appear brighter, as brightness decreases with the square of the distance.
Step-by-step explanation:
Two stars with the same luminosity can have different apparent brightness due to their distance from the observer. Luminosity is the total energy output of a star, while apparent brightness is how much of that energy reaches an observer on Earth. If you imagine stars as 25-watt bulbs, they all emit the same amount of energy, but the closer bulbs appear brighter because less light has spread out before reaching you. Similarly, a star that is closer to Earth will appear brighter than a star that is further away, even if they both have the same luminosity.
Using an example, if Star A and Star B have identical luminosities and Star A is 20 light-years away while Star B is 40 light-years away, Star A would appear brighter. This is because the apparent brightness of a star decreases with the square of the distance to it. In this case, Star B would appear four times fainter than Star A because it is twice as far, and brightness drops by the square of the distance (2 squared equals 4).