What is the focal length of the mirror?

[dorado29]

Homework Statement

A 2.0 cm tall object is placed in front of a mirror. A 1.0 cm tall upright image is formed behind the mirror, 165 from the object

Homework Equations

1/s + 1/s' = 1/focal length

h' / h = magnification

-s' / s = magnification

h' / h = s' / s (i found this online so I'm not sure if it's correct)

The Attempt at a Solution

I'm pretty sure the question is saying the total distance from the object to the object's image is 165cm so:

s' + s = 165cm

s' = 165cm - s

then i plugged that into h'/h = s'/s

1cm/2cm = (165cm - s)/s and solved for s and got 110 cm so distance from object to mirror is 110 cm and distance from mirror to image is 55 cm

then i did 1/s+1/s'=1/f and solved for f

1/110cm + 1/55cm =1/f and got f=36.6cm. This was incorrect, so now I'm not sure what I should try

 

[rl.bhat]

Given mirror is a convex mirror. So check the sign convention of the object distance , image distance and the focal length.