- #1
cclement524
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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
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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!