At what distance from a concave mirror of focal length 10cm should an object 2cm long be placed in order to get an erect image 6cm tall?

Given

Focal length of concave mirror f = -10 cm
Height of the object ho = 2 cm
Height of the image hi = 6 cm

We need to find the object distance

So we know that
Magnification m = hi/ho = 6/2 = 3 (erect image)
m = -v/u
3 = -v/u

⇒ v = -3u
Let us now consider

Mirror formula: 1/v + 1/u = 1/f
1/(-3u) + 1/u = 1/(-10)
⇒ u = -20/3 = -6.7 cm

So At -6.7cm distance from a concave mirror of focal length 10cm should an object 2cm long be placed in order to get an erect image 6cm tall.

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