Trouble with mirror equations, .

[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

 

[Doc Al]

1/do+1/di=1/f

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

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

 

[x64bob]

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

 

[Doc Al]

so doesn't "- di/2.2" mean that both di and 2.2 are negative values?

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.

 

[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?

 

[Doc Al]

what about convex mirrors? can i use exactly the same equations for them?

The basic equations are the same.

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?

A negative magnification means that the image is inverted, but a negative radius just means that the mirror is convex.

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?

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.