Certainly many of us heard this song “Aadha hai Chandrma raat aadhi” from 1958 film Navrang by V Shantaram.
And many, in particular old-timers, would remember the actual scene. If you have not then you can search for the song on the YouTube.
With all due respect to that great man he was in his field VS committed a big blunder during the picturization of the song.
lyricist Bharat Vyas, when he wrote “Aadha hai Chandrama” what should be having in his mind is that the Moon is half illuminated by the sunlight. The day is, therefore, either the first quarter or the last quarter of the Moon
One can be sure that by those lines the lyricist did not possibly mean that the angular diameter of the moon was half nor that the Moon is broken into two equal parts and only one half is presented to the ‘observer’.
The Raat Aadhi signify the time when the scene is enacted and it is the midnight.
Putting these two together the only possible direction where the moon can be seen at this time is at the horizon – either the moon is rising, if it is last quarter or is setting if it is the first quarter.
AND what do we see – a crescent moon two or three days before or after the new moon phase.
I suppose the people are lost in the song and no one seems to be bothered by astronomical blooper.
Well check out this link for first and last quarter phase of the Moon – click here.