The appearance of a half moon in the night sky is caused by the relative positions of the sun, Earth, and moon. Here's the breakdown:

* Sun's Light: The moon doesn't emit its own light. We see it because sunlight reflects off its surface.

* Phases: As the moon orbits the Earth, the angle at which sunlight hits it changes. This creates the different phases of the moon we see.

* Half Moon: When the moon is at a 90-degree angle to the sun and Earth, we see half of its illuminated surface. This is called the first quarter or last quarter moon, depending on which side is illuminated.

Visualizing the Half Moon:

Imagine a half-circle. One side of the circle represents the illuminated portion of the moon as seen from Earth. The other side is the dark, unlit portion.

To remember which side is illuminated:

* First Quarter: The illuminated side is on the right as seen from the Northern Hemisphere.

* Last Quarter: The illuminated side is on the left as seen from the Northern Hemisphere.

Let me know if you'd like a more detailed explanation of lunar phases!