that side that we are seeing is 1/2 lit up by the sun, and the other 1/2 in darkness.
Half of it, the same as always. Half of the visible side of the Moon will be brightly lit by the Sun, and the other half is often dimly visible by reflected earthshine, sunlight that is reflected from the Earth and then shines down on the night side of the Moon.
Two weeks after a full moon, the moon would appear as a waning gibbous, with more than half but less than fully illuminated. It would be visibly less bright than during a full moon, with a larger portion of the left side darkened.
If you are on the moon at the time of "New Moon", and you are facing the earth, you see a "Full Earth". If you stay up there a while, and call your partner on earth every day, and you describe to each other what you're seeing, you'll notice something very interesting: The part of the moon that HE sees, plus the part of the earth that YOU see, always adds up to a complete circle of illumination. Each of you sees the part of the circle that the other one is missing.
A half moonA half moon
The two phases of a waxing Moon are the first quarter and gibbous. During the first quarter, half of the Moon is illuminated and appears as a half-circle in the sky. During the gibbous phase, more than half but not yet fully illuminated, the Moon appears as a large, slightly bulging shape.
Assuming you're asking how often a "half moon" appears, a half moon (First or Third Quarter moon) will usually occur every 14-15 days (half a lunar month).
First quarter and last quarter appear as a half moon. about halfway down this page are some pictures: http://www.calculatorcat.com/moon_phases/moon_phases.phtml
At the time of the "First Quarter" and "Third Quarter" phases, the moon appears half-illuminated. These occasions are roughly 7 days and 21 days after New Moon respectively, and Full Moon occurs at the time exactly midway between them. Note: Both phases are easily visible in the daytime. First Quarter rises in the east around Noon, and Third Quarter sets in the west around Noon.
The moon in the days before and after a full moon appear as a gibbous moon. A gibbous moon is anything between a full moon and a half moon.
Half of it, the same as always. Half of the visible side of the Moon will be brightly lit by the Sun, and the other half is often dimly visible by reflected earthshine, sunlight that is reflected from the Earth and then shines down on the night side of the Moon.
From a great height, Japan would be appear to be in the shape of a "half moon."
Somewhere between half and all of the visible part of the Moon will be bright in that case, depending on the exact position of the Moon.
You can often see the entire "near side" of the Moon, because even though the sunlit half is very bright, the other part is dimly lit by reflected Earthlight. However, the official answer to your question is probably "one quarter". You can only see one-half of the Moon, and only half of that is lit up by the Sun.
Two weeks after a full moon, the moon would appear as a waning gibbous, with more than half but less than fully illuminated. It would be visibly less bright than during a full moon, with a larger portion of the left side darkened.
quarter Moon if its half of a sphere then its half moon
If you are on the moon at the time of "New Moon", and you are facing the earth, you see a "Full Earth". If you stay up there a while, and call your partner on earth every day, and you describe to each other what you're seeing, you'll notice something very interesting: The part of the moon that HE sees, plus the part of the earth that YOU see, always adds up to a complete circle of illumination. Each of you sees the part of the circle that the other one is missing.
It will appear as a Gibbous moon (3/4 of a full moon).