# Curved mirrors (Optics).

1. Nov 23, 2007

### wiz0r

1. The problem statement, all variables and given/known data
Ok, so my profesor asked my to prove this;

Prove that f = R/2. To prove it geometrically.

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............. F ......)
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Ok, so I have that curved convave mirror, now I need to prove that f = R/2, where R is the radius of the circle, and f is the focal lenght.

3. The attempt at a solution
Um, well I can't understand why is it R/2, and not just R, I'll post whatever I'll find while doing research. But, please, can anyone help me get started? Or just explain it to, I'd be really grateful. Thanks!!

Last edited: Nov 23, 2007
2. Nov 23, 2007

### wiz0r

ok, I've got a better picture;

http://en.wikipedia.org/wiki/Image:Concave_mirror.svg

I can see it better now, why f = r/2, but, why? how can i prove it?

the center of curvature is the center of the circle, so obviously the focus = r/2, but how can i prove this geometrically?

3. Nov 23, 2007

### wiz0r

4. Nov 24, 2007

### wiz0r

anyone?

5. Nov 24, 2007

### Staff: Mentor

I suspect that your professor wants you to apply the law of reflection (and a bit of geometry) to derive the focal length of a concave mirror. That last link does it for you, but I suggest you rederive it for yourself.