Is there any instrument that can photograph a virtual image? How would such a device work?
Yes. Any camera that's capable of photographing actual objects is also capable of photographing real and virtual images. If you stand in front of a mirror and take a photo, you'll get a photo of the virtual image.
What the camera does is to take the image and make a secondary image of it (an image of the image). This secondary image is a real image, because it has to be projected onto the film or chip inside the camera. The same thing happens in your eye. When you look at yourself in a mirror, your retina gets a real image of the virtual image.
(I don't have enough rep to leave comments yet, so I have to leave this as an answer...)
What makes an image "virtual" is that it is not a physical source of light or of reflected light. As Mr. Crowell points out, virtual images can be photographed; light does appear to come from them. However, a virtual image cannot be projected, since the light rays are diverging from that "apparent source"; some additional optical device must cause the rays to converge elsewhere in order to produce a real image which can be recorded.
A real image only exists in one location. ie Where the light rays converge. Virtual images exist in many locations . To see a real image you have to stand at the focal point but you can view virtual images from different angles. NB, a real image would be formed on our retina but the eye is more like a camera and the screen is in the optic centre at the back of our brain. This is where the images we see are created. We see a virtual image of our surroundings.