This is a clever toy consisting of two concave parabolic mirrors, one on top of the other, facing each other. The mirrors are made so that the focal point of one mirror is right at the surface of the other. You place a small object on the surface of the bottom mirror (inside the thing, where you can't see it directly). Since light from the object is at the focal point of the top mirror, the light reflects off the top mirror as parallel light, which then reflects off the bottom mirror to focus at its focal point: which is the the surface of the top mirror. Of course, a hole is cut out of the top mirror so that the real image can be seen. The real image looks like the object is really there.
I'm still a bit confused though; it might be just some semantic problems. When you say "virtual image" do you really mean virtual image as in the image that's behind the mirror? If that were so, how we see a projection of it? Also, if the image is at the focal point, doesn't that reduce the size of the image?
What makes you think that the image will be half the size?
Note that light from the object isn't exactly at the focal point, since it's an object not a point source. According to my calculations, if the object is small enough (compared to the focal length) the image will be the same size as the object.