Do vampires have a reflection or not? Also wouldn't the moon hurt them?
Both excellent questions. I'll start with the second one first.
You are right to wonder if moonlight would hurt a vampire since moonlight is actually sunlight being reflected off of the Moon toward Earth. Since sunlight contains ultraviolet rays (both UV-A and UV-B), it's no surprise to discover that moonlight does as well. We know that the ultraviolet rays in sunlight are highly damaging to vampire skin, so doesn't it reason that the ultraviolet rays in moonlight would be as well?
Technically this is all scientifically correct. The only problem with the argument is that moonlight has far too little ultraviolet in it to do damage - even to a vampire. A good portion of sunlight (around 1/3) is reflected off of the Earth back into space. With moonlight we aren't getting any direct rays, just the ones that are reflecting off of the moon in our direction, and some of those end up reflecting off of our planet still, and then much of what's left is absorbed by the atmosphere. All in all moonlight ends up being about 500,000 times weaker than sunlight, meaning that anyone (human or vampire) will absorb fewer ultraviolet rays by staying out all night in the moonlight than spending a single second under the sun.
The other question is a bit more tricky. It has been long included in vampire mythology that vampires neither have a reflection nor cast a shadow. While this may seem odd in today's world, this folk wisdom made a lot of sense centuries ago.
Long ago in Europe, most people believed that the image seen in a person's reflection was actually their soul. This is why, when people died, mirrors would be either turned around or covered, and containers of water (also reflective), would be emptied. It was thought that the soul was rise after death, but if it saw its own reflection it would be trapped inside the mirror (or water) forever. In places like Romania, windows were often opened to help spirits leave the residence and move onto the afterlife. In other cultures, pots of water were placed near grave sites to capture rogue spirits based on this same reflection concept.
Of course we know now that a reflection is not a supernatural event, but the effect of light bouncing from one place to another. Since vampires are corporeal creatures (having a physical body), physics tells us that they must reflect light in the same way that any other object does. If this is true, then why does vampire mythology tell us that vampires don't have a reflection?
Well, we know that vampires don't have souls, and if a reflection was thought to be that of a soul, then it makes sense that our ancestors would believe that vampires would have no reflection. No soul = no reflection. Same with a shadow, where the logic fell under the same reasoning.
I tend to think that if a vampire were here right now looking into a mirror they would be able to see their reflection, as would anyone else. That doesn't mean that a vampire would want to see their reflection, though. If anything were going to be a reminder of their living curse, it would have to be looking into your own soulless eyes staring back at you.