At what distance is the object from the mirror?

[dmolson]

Homework Statement

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?

Homework Equations

1/p + 1/q = 1/f

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.

 

[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.

 

[Doc Al]

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

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.

I obtained 16.25 using equation 1/p -1/32.5 = -1/32.5, but it is wrong, as well as -16.25.

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.)