An image of an object obtained by a convex mirror is n times smaller than the object. If the focal length of the mirror is f, the object distance would be .

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(3) (n-1)f. Given: a convex mirror of focal length f, and an image n times smaller than the object, so the magnification is m=1/n. Idea: take f positive for the convex mirror and u as the object's distance in front of it; the mirror formula then turns m=-v/u into m=f/(f+u). That form already tells the story: m is positive and less than one, so a convex mirror always gives a virtual, erect, diminished image. Set f/(f+u)=1/n nf=f+u u=(n-1)f Check it at n=2: the object stands at u=f, and an object at the focal distance of a convex mirror does give a half-size image.

An image of an object obtained by a convex mirror is n times smaller than the object. If the focal length of the mirror is f, the object distance would be ________.

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