For those of you who have never used one, a cosmetic mirror is a mirror that creates a magnified image. Usually they are small and hand held so you can use them to apply things like eye liner and see what you are doing.
I am embarrassed to say, while we had the right instincts in this matter, it took us a day to figure out how to do the ray tracing to prove we were right, so I figured I'd make a blog post out of it.
To start with, let's examine the three types of basic mirrors. There is the flat mirror, which is the kind that hangs over your bathroom sink and is the kind of mirror pretty much everyone is familiar with. It can not magnify, either positively (make it bigger) or negatively (make it smaller). So that one's out.
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| Don't you love my white board illustrations? |
There is the convex mirror, which is bowed outward and is the kind you see in gas stations as a security measure. They create smaller, distorted images of whatever is in front of it. So that's out.
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| No? Too bad. |
Lastly, there is the concave mirror, which bows inward. This is the most complicated mirror, because what it does depends on what region you are in, as shown below.
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| I do need new markers though.... |
So this is the kind of mirror we need, and we know we need to be inside the focal point for this to work. That's fine, because you are usually holding this close to your face anyway. However, the image that it creates is imaginary, and that's the part that was tripping us up while we were drawing the ray diagram.
As you can see, to demonstrate the effect we know occurs, we need to trace partially real rays, and partially imaginary rays. The imaginary rays are what we perceive happens, the virtual image that is created 'in' the mirror.
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| Diagram a la Hecht |
So there you have it. How a cosmetic mirror works. Incidentally, this also applies to the image created in bowl of spoon. See if you can find the focal point!
~AMPH
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