For a concave mirror of focal length f, image is 2 times the size of the object. Then the object distance from the mirror may be
Question
For a concave mirror of focal length f, image is 2 times the size of the object.
Then the object distance from the mirror may be:
Solution
The magnification (m) of a mirror is given by the ratio of the image height to the object height. For a concave mirror, this is also equal to the negative ratio of the image distance (v) to the object distance (u).
So, m = -v/u
Given that the image is 2 times the size of the object, the magnification is -2.
So, -2 = -v/u
Rearranging, we get v = 2u.
The mirror formula for a concave mirror is given by 1/f = 1/v + 1/u.
Substituting v = 2u into the mirror formula, we get 1/f = 1/(2u) + 1/u = 3/(2u).
Rearranging, we get u = 3f/2 or 2f/3.
So, the object distance from the mirror may be either 3f/2 or 2f/3.
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