Half Moon – why does the shadow look straight?

When my 10 year old was about 5 he asked me “when it’s half moon, why does the shadow look straight?”

I asked a friend at the time who told me to tell him this:

Half moon is still curved, but only looks straight. Optical illusion.

When the moon is reflecting more light when the earth first starts to cause a shadow, the dark area is more pronounced, plus it’s only covering part of the curvature of the moon, so the shadow looks smaller and more defined.

By the time of half moon, a larger part of the circumference of the earth is casting the shadow and the curve is less pronounced. Plus, with less light reflecting back, the sharpness of the shadow image on the moon is reduced.

Added to this, the moon is also curved, which means the shadow disappears over the moon horizon. Together they make it look straight to the naked eye.

This satisfied the 5 year old (although many other questions followed) but even now I look up at the half moon and see that oh so straight line, I still frown and think how?!

I also can’t think about it without the Jaffa Cakes advert running repeatedly through my head – do you remember it?