An object 82 cm high forms a virtual image 4.1 cm high located 4.6 cm behind a mirror. find the object distance.

The object distance is 92 cm.  

Explanation:

let v be the image distance and h be the height of the image, let u the be the object distance and H be the height of the object.

then, the magification of the mirror is given by:

m = -v/u and m = h/H

so, -v/u = h/H

         u = -v×H/h

            = -(-4.6)×(82)/(4.1)

            = 92 cm

Therefore, the object distance is 92 cm.