Question

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

Answer 1

the object should be placed between focus and pole.

Answer 2

Focal length of concave mirror f = -10 cm
Height of the object ho = 2 cm
Height of the image hi = 6 cm
Magnification m = hi/ho = 6/2 = 3 (erect image)
                         m = -v/u
                          3 = -v/u   ⇒ v = -3u
Mirror formula: 1/v  +  1/u   = 1/f
                           1/(-3u) + 1/u  = 1/(-10)
                            ⇒ u = -20/3 = -6.7 cm

So the object should be placed at a distance of 6.7 cm from the pole of the concave mirror (on the left, in front of the mirror).



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