Shaukat A study of science of moon-sighting can clarify lots of misconceptions and wrong perceptions.
Most people associate visibility with the age of the moon.
Age of the moon is simply the time lapsed since new moon. It can give a rough approximation for visibility. The visibility depends upon the angular separation of the moon from the sun seen from the earth. As the time passes from the instant of new moon, the angular separation between the sun and the moon increases. This angular separation reflects sun's light to earth.