How are objects reflected in a mirror, and how do our eyes focus on the object?

Mat:

Here is one that has always bugged me. It seems logical that when I look at something in a mirror, the critical distance my eyes should have to focus is between me and the mirror (the reflected information should come to the mirror untainted). An example of this would be for me, the nearsighted one, standing two feet from the mirror, would see the reflection in focus because I am only looking at something two feet away, like looking at a picture of something far away. I know from observation that this is not so. Things in the mirror are focused at the distance from me to the mirror plus the mirror to the object (I think). This doesn't make sense to me. Two questions: Where is the fault in my logic, and if you set up a camera to bring an object the distance of the mirror away in focus and then took a picture of the mirror, would all the objects in the mirror be out of focus? Soon I will be able to sleep at night.

— Joe R., the Net

Thanksgiving preparations (peeling the cranberries, grief counseling for the turkeys) has the place in an uproar. There's an outside chance we have your question a little out of focus, although the elves took a vote on what exactly it all means. They held it up to the light, read it backwards in a mirror, and took it out for a drive and paid a buck to one of those squeegee guys to scrub it up a bit... But we always like a challenge, so here's what we came up with. The reflection does come to you more or less "untainted," if we can assume you're not looking into a very cheap mirror with lots of pits and a dull reflective surface. But the mirror is reflecting light that has traveled varying distances. If you're looking into a mirror, with a birthday cake 3 feet behind you and a goat 10 feet behind you, the goat light travels farther to reach the mirror than the birthday cake light. So, when you stand 2 feet from the mirror, you're looking at birthday cake light that's traveled 3 feet to the mirror, then 2 feet to your eyes; goat light has traveled 12 feet, 10 plus 2. The farther the light travels, the weaker the image, whether it's traveling to your eyes or to the mirror. If you can't see the goat clearly when you look at it directly, you won't be able to see it when you look in the mirror.

Actually, when your optometrist puts you in that small, dark room to check your distance vision with an eye chart projected on the wall, the light that forms the chart has bounced several times across the room off a series of mirrors. By the time it hits the wall, it's traveled 20 feet, or whatever the selected distance is. Otherwise, we'd have to have our vision checked in a bowling alley.

The image formed on the surface of a plane mirror is called a virtual image. The light you see is coming from the mirror, in the strength it reached the mirror, but our eye-brain connection creates the world behind the mirror, with a hazy goat on the distant horizon probably eating your birthday cake.