Calculating the Image Height from a Double-Sided Spherical Mirror

[theintarnets]

Homework Statement

A man holds a double-sided spherical mirror so that he is looking directly into its convex surface, 44.8 cm from his face. The magnification of the image of his face is +0.22. What will be the image distance when he reverses the mirror (looking into its concave surface), maintaining the same distance between the mirror and his face?

Homework Equations

m = -d_i/d_o
1/f = 1/d_i + 1/d_o

The Attempt at a Solution

First I solved for the focal length like this:

d_i = - (m*d_o)
d_i = - (.22*44.8) = -9.856 cm

1/f = 1/d_i + 1/d_o
1/f = 1/-9.856 + 1/44.8
f = -12.64 cm

Then I tried to solve for the image height of the concave side:

1/d_i = 1/f - 1/d_o
1/d_i = 1/-12.64 - 1/40.8
d_i = -9.856 cm

But the answer should have been 17.6, I don't really know what to do. Please help?

 

[theintarnets]

Oh, I think I got it! I think the signs in the formula switch to + for concave surfaces. When I do 1/di = 1/-12.64 + 1/44.8 I get -17.6. But I think my signs are wrong altogether, because it's supposed to be positive...