Note that in this picture, I am using my EF-S 50-250mm f/4-5.6 IS II lens, while my girlfriend has on her EF 70-200mm f/2.8L USM lens on. Notice anything fun about it?
Did you say "Oh, I know, iforgotmyusernameonce! You're in focus in the reflection from her lens but her hair in the background is also in focus! Why is that? Is this shopped?"
No, it's not photoshopped. The fun thing about this picture is that the distance between the end of my lens and the end of her lens (the plane on which the reflection is projected on) is equal to the distance from the end of her lens to her hair.
That's an easy enough concept to grasp, right? No?
[WARNING! SCIENCE AHEAD!]
When an image is reflected on a flat plane (such as a mirror, or in this case, a polarizing filter), the distance in which you actually see the image is equal to the distance from which you are standing away from it.
That even confused me, and I wrote it.
Imagine this. You're standing in your bathroom, looking into your flat mirror. You see an image of you reflected back towards you. When you step away from the mirror, your reflection also backs away from the flat plane that is the mirror. Let's call this point 0.
If you think of the mirror like a number line (remember those from elementary school, when you first started learning about negative numbers?) where the surface of the mirror is at 0 and the distance between you and that mirror is x, the reflected image (the virtual image) will be -x. You will have to focus at 2x (2 times the distance between you and the mirror) to focus on the image in the mirror.
Here's an image that might explain this concept:
Because I was standing exactly the distance from her lens as her lens was from her hair, both the virtual image (the reflection) and her hair are in focus.
Yay for fun with optics!