# Trouble with mirror equations, need help.

1. Oct 1, 2006

### x64bob

heres the problem:
a dentist wants a small mirror that, when 2.20cm from a tooth, will produce a 4.5x upright image. what kind of mirror must be used and what must its radius of curvature be?

so i did the following calculations with the mirror equations i learned:

m=4.5

equation to get the di https://www.physicsforums.com/attachment.php?attachmentid=7885&stc=1&d=1159712057

4.5*(-2.20) = di di=-9.9

1/do+1/di=1/f

1/(-2.2) + 1/(-9.9) = 1/f

1/(-2.2)=(-0.454545455)
1/(-9.9)=(-0.101010101)

(-0.454545455)+(-0.101010101)=(-0.555555556)

1/(-0.555555556)=f

1/(-0.555555556)=(-1.8)

f=(-1.8)

f2 = r

-1.8 * 2 = -3.6

so the radius is -3.6 and i guess it is concave as only concave mirrors 1.0+ magnify? that's wrong as my book says the correct answer is 5.66cm, concave. what am i doing wrong

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2. Oct 1, 2006

### Staff: Mentor

The object distance should be +2.2, not -2.2.

3. Oct 2, 2006

### x64bob

ok, thanks alot. so doesn't "- di/2.2" mean that both di and 2.2 are negative values?

4. Oct 2, 2006

### Staff: Mentor

Not sure what you mean. Think of it this way. You know that do is positive: do = +2.2 cm. The magnification is positive, since the image is upright: m = +4.5. Since m = -di/do, that tells you that di is negative: di = -m*do = -9.9 cm.

5. Oct 2, 2006

### x64bob

what about convex mirrors? can i use exactly the same equations for them? on my next task (m=0.33 do=20) i had to calculate the radius for this convex mirror and i got -19.7, so if - means that the image is inverted, and as far as i know convex ones don't generate inverted images, should i remove the - or something?

and does a magnification of 2.0 mean that the di is just twice as short as do while m0.5 means that di is twice as long as do?

6. Oct 2, 2006

### Staff: Mentor

The basic equations are the same.
A negative magnification means that the image is inverted, but a negative radius just means that the mirror is convex.

No, just the opposite. Review the definition of magnification, given by the equation: m = -di/do

So a magnification of 2.0 means that di is twice as long as do.