# Solving a convex mirror problem

**1. The problem statement, all variables and given/known data**

Given the following information: convex mirror, focal length (f) = 12.5 metres, height object (h_{o}) = 5 metres, height image (h_{i}) = 1 metre. Find distance object (d_{o}) and distance image (d_{i}).

**2. Relevant equations**

1/f = 1/d_{o} + 1/d_{i}

Magnification= -h_{i}/h_{o} = d_{i}/d_{o}

**3. The attempt at a solution**

I found that the magnification is -0.2.

Rearranging the magnification equation I found that d_{i}=-0.2do

and that

do=-5d_{i}

My intention was to substitute one of the two into 1/f = 1/d_{o} + 1/d_{i}

I tried to make the denominators equal after substituting in d_{i}=-0.2do however my answer was incorrect.

Correct answers are d_{o} = 50 metres, d_{i} = -10 metres

I don’t understand how to mathematically solve this problem. Any help would be greatfully appreciated.

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