# Convex mirror find object distance

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1. Mar 17, 2015

### xamy

1. The problem statement, all variables and given/known data
An object is placed in front of a convex mirror with a 45.6-cm radius of curvature. A virtual image half the size of the object is formed. At what distance is the object from the mirror?

2. Relevant equations
1/f=1/d0+1/di
hi/h0=-di/d0

3. The attempt at a solution
hi=-1/2h0
f=45.6/2=22.8

di=-1/2d0

1/22.8=1/d0-2/d0
d0=-22.8

This is my solution but this is nor correct.....anyone plz tell me the mistake. thanks!

2. Mar 17, 2015

### Suraj M

Firstly please use brackets, it looks like it may be $d_i=\frac{-1}{2d_o}$or $d_i=\frac{-1}{2}d_o$
and i don't see the need for the -ve sign in the above equation(logically).
Also because when you substitute the $h_i$ you should negate it as it is inverted, so there shouldn't be a -ve sign for your above equation

3. Mar 17, 2015

### xamy

ok so after editing the ans becomes
1/22.8=1/d0+2/d0
d0=68.4

4. Mar 18, 2015

### Suraj M

I'm sorry i correct myself, i thought it was a concave mirror, so you shouldn't negate $h_i$ as it is erect.
you were right. The answer you have obtained, looks to be right. Why do you feel it is wrong?

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