Quarter moon (first quarter lunar phase)
Photograph by MCN, 2015

In astronomy, the moon phases are defined by its position in its orbit around Earth. During the first quarter and third quarter phases, we see exactly half of the illuminated side of the moon, representing a quarter of its complete orbit around Earth. The first quarter moon rises around midday and sets around midnight, visible in the afternoon and evening sky. The right half is illuminated in the Northern Hemisphere and the left half in the Southern Hemisphere. The third quarter moon rises around midnight and sets around midday, visible in the morning and early afternoon sky. The opposite side is illuminated as compared to the first quarter. In common usage, the term 'half moon' loosely describes both the first and third quarter phases. Though not incorrect, but it does not fully capture the moon's orbital position.