The moon is halfway through the waxing crescent phase. in approximately how many days will it be in the last-quarter phase?

The moon takes 18 days to change its phase from halfway through the waxing crescent to the second quarter.

Waxing crescent phase is the phase of the moon that starts after the New Moon and lasts until the First Quarter.

We know that it takes 15 days for the moon to be halfway through the waxing crescent phase.

Now, the time taken by the moon to change phase from halfway through waxing crescent and first quarter is 3 days.

Hence

Therefore, the moon takes 18 days to change its phase from halfway through the waxing crescent to the second quarter.

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Let's say the Moon's complete cycle of phases is about 28 days (4 weeks) ... just so the arithmetic is easier. (Close enough. It's actually 29.53 days.)

If it's halfway through the waxing crescent, then it'll reach first quarter in 3 days or so.

From there, it'll take the next 7 days to become Full, and another 7 days to reach last quarter.

Total from half-waxing-crescent to last quarter . . . about 17 days.

54 degrees incident angle = reflected angle

angle is from normal turned to line of ray