At what distance is the object from the mirror?

  • Thread starter dmolson
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  • #1
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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.
 

Answers and Replies

  • #2
hage567
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"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
Doc Al
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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.)
 
Last edited:

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