What will be the image distance when he reverses the mirror ?

[cclement524]

Homework Statement

A man holds a double-sided spherical mirror so that he is looking directly into its convex surface, 47.4 cm from his face. The magnification of the image of his face is +0.18. 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? Be sure to include the algebraic sign (+ or −) with your answer.

Homework Equations

mirror formula> 1/f = 1/v + 1/u
f = vu/(v+u)
v> image, u>object, f> focal
-----------------

m = magnification = - v/u

1/f = 1/v + 1/u
v = fu/(u-f)

The Attempt at a Solution

mirror formula> 1/f = 1/v + 1/u
f = vu/(v+u)
v> image, u>object, f> focal
-----------------
convex> u = - 47.4,
m = magnification = - v/u = - v/(-47.4) = +0.18
v = 8.532
f = 8.532*47.4/8.532-47.4 = 7.23
-----------------------------
it has to be assumed that radius of curvature (R = 2f) is same
concave>
f = - 7.23
u = - 47.4 (same)
1/f = 1/v + 1/u
v = fu/(u-f)
v = concave = (-7.23)(-47.4)/[- 47.4+ 7.23]
v = concave = - 8.53129cm
m = - 8.531 /47.4 = - 0.17998


I am getting the wrong answer with the wrong sign somehow, but I don't know where I went wrong. Any help would be greatly appreciated. Thank you!

 

[ideasrule]

By convention, object distance should always be positive for a real object. The focal length should be negative for a convex mirror and positive for a concave one. If you flip all your signs around, you'll get the right answer.

 

[cclement524]

I am still getting a decimal answer, but the answer is somewhere around 10. Is there anything else I should be doing differently?