Question

the focal length of the concave mirror is 30cm.find the  position of the object in front of the mirror so that the image is 3 times the size of the object

Answer 1

1/v + 1/u = 1/f
Let the image be real.  v is -ve. u is -ve. f is -ve.

v = 3 u      as magnification m =  -v / -u = v/u

1/(-3u)  + 1/(-u)  = 1/(-f)

-4/3u = 1/(-30)  =>  u = 40 cm  that is 40 cm infront of the mirror.

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Let the image be virtual.    so v/u = -3
v is +ve  u is -ve    f is -ve

v = 3u
1/3u - 1/u = -1/f
-2/3 u  =  -1/30    u = 20 cm  that is 20 cm in front of mirror.

Answer 2

f= -30 cm m= 3

U = ? V= v cm

$m \: = \frac{ - v}{u} \\ 3 \: \: \: = \frac{ - v}{u} \\ 3u \: = - v$

$\frac{1}{f} = \frac{1}{u} + \frac{1}{v} \\ \frac{1}{f} = \frac{v + u}{u \: v} \\ \frac{ - 1}{30} = \frac{ - 2}{ - 3u} \\ 3u = 30 \times - 2 \\ u = \frac{30 \times - 2}{3} \\ u \: = - 20cm$

Thus the object should placed 20 cm from the front of mirror.