# Optics Question

1. Mar 26, 2007

### dmolson

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

An object is placed in front of a convex mirror with a 65 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/p + 1/q = 1/f

3. The attempt at a solution

I have tried this problem several times different ways and cannot get the correct solution. I tried it this way.

focal length = Radius of curvature/2 = -32.5 cm (negative because convex mirror
virtual image = 1/2 object = -q
object = + p

I obtained 16.25 using equation 1/p -1/32.5 = -1/32.5, but it is wrong, as well as -16.25. Any help would be great.

2. Mar 26, 2007

### hage567

"virtual image = 1/2 object = -q"

You didn't use this correctly in your calculation. The question says the image is half the size of the object, so that means q = -0.5p. You can use that in your equation. I don't understand why you have -1/32.5 twice there.

3. Mar 26, 2007

### Staff: Mentor

You're on the right track here, but you didn't follow through. Hint: Write the image distance (q) in terms of the object distance (p). Then apply that to the mirror equation.

Not sure what you are doing here. Redo this given my advice above. (And realize that a negative value of p would imply that the object was inside the mirror!)

(Looks like hage567 beat me too it while I was daydreaming.)

Last edited: Mar 26, 2007