Using a good pair of binoculars, you observe a section of the sky where there are stars of many different apparent brightnesses. You find one star that appears especially dim. This star looks dim because it is:.

Using a good pair of binoculars, you observe a section of the sky where there are stars of many different apparent brightnesses. You find one star that appears especially dim. This star looks dim because it is farther away or it has a small radius.

Explanation:

Apparent magnitude in astronomy is the apparent brightness of a star that is seen from the Earth, that brightness can variate according to the distance at which the star is from the Earth or due to its radius.

That can be demonstrate with the next equation:

(1)

Where F is the radiant flux received from the star, L its intrinsic luminosity and r is the distance.

For example, an observer sees two motorbikes approaching it with its lights on but one of the motorbikes is farther, so the light of this one appears dimmer, even when the two lights emit the same amount of energy per second.  

That is because the radiant flux decreases with the square distance, as can be seen in equation 1.

In the other hand, a bigger radius means that the gravity in the surface of the star will be lower, allowing that light can escape more easily:

(2)

Where g is the surface gravity in the star, G is the gravitational constant, M is the mass of the star and R is the radius of the star.