Odd optics of glasses & convex mirror

Factual Questions
1

Hey CalMeacham, you listening?

I just got my first pair of progressive bifocals and am trying to get used to them. I was wearing them driving my car to work and noticed something very strange.

I was glancing into my left-side mirror without turning my head, and so the view in the mirror was not focused. When I turned my head so as to align the distance portion of the glasses towards the mirror, the objects in the mirror came into focus. This is normal and expected. However, I also have one of those stick-on convex mirrors stuck on the corner of the mirror. The objects in the convex mirror were blurry. I would have expected them to focus also.

Here’s the really odd part. When I tipped my head up so as to align the reading portion of the glasses with the convex mirror, the objects in the convex mirror came into focus, and the objects in the flat mirror returned to be blurry.

Does the convexity of a mirror somehow affect how reflected objects are focused? I would have thought that the virtual image reflected in a convex mirror is still far away, but in this case it seems to be the opposite. Is it possible that that a virtual image of something relfected in a convex mirror could be at arm’s length?

Just to fill in the facts, the prescription on these glasses is very weak, both bottom & top. I can drive/read without them but it sharpens signs up noticeably.

2

Is it possible that that a virtual image of something reflected in a convex mirror could be at arm’s length?

Yes. The virtual image in a convex mirror is always ‘closer’ to the plane of the mirror than the object being reflected. If the mirror is curved enough, as in the case you describe, the image of a distant object can easily focus at reading distance.

3

Yes, the image in a convex mirror forms in front of the focal point (which is in front of the center of curvature). Those little stick-on mirrors have a pretty tight curve, so I’d guess the image is a few inches past the mirror (from your point of view).

Here is a java applet showing the optics of a convex mirror:
http://www.physics.uoguelph.ca/applets/Intro_physics/kisalev/java/dmirr/

4

CookingwithGas: Sorry, I got here late. But it looks like other folks have covered this.

BTW, progressive lenses have weird shapes. I have to confess that I still don’t understand why exactly they’re made the way they are.