12-01-2016, 01:26 PM
If the moon's surface were like a perfectly smooth billiard ball, its surface brightness would be the same all over. In such a case, it would indeed appear half as bright.[Phases of the Moon Explained]
But the moon has a very rough topography. Especially near and along the day/night line (known as the terminator), the lunar landscape appears riddled with innumerable shadows cast by mountains, boulders and even tiny grains of lunar dust. Also, the moon's face is splotched with dark regions. The end result is that at first quarter, the moon appears only one eleventh as bright as when it's full.
The moon is actually a little brighter at first quarter than at last quarter, since at that phase some parts of the moon reflect sunlight better than others.
But the moon has a very rough topography. Especially near and along the day/night line (known as the terminator), the lunar landscape appears riddled with innumerable shadows cast by mountains, boulders and even tiny grains of lunar dust. Also, the moon's face is splotched with dark regions. The end result is that at first quarter, the moon appears only one eleventh as bright as when it's full.
The moon is actually a little brighter at first quarter than at last quarter, since at that phase some parts of the moon reflect sunlight better than others.