The image formed is real (convex lens forms diminished real image)
m= -2/3
v= + 12cm
m=v/u
-2/3=12/u
-2u=36
u= -18 cm
now
focal length formula
1/f= 1/v - 1/u
1/f= 1/12 - 1/(-18) = 5/36
f=36/5
focal length of the lens= 7.2cm
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Answers & Comments
or, magnification = size of image/ size of object = v/u
or, -2/3 × size of object/size of object = v/u
or, -2/3 = v/u
or, u = (3/2)v = -1.5v ..........(1)
image distance , v = 12cm
object distance , u = -1.5v = -1.5 × 12 = -18cm
use formula, 1/v - 1/u = 1/f
or, 1/12 - 1/-18 = 1/f
or, 1/12 + 1/18 = 1/f
or, 1/f = 5/36
hence, f = 7.2 cm
Verified answer
The image formed is real (convex lens forms diminished real image)
m= -2/3
v= + 12cm
m=v/u
-2/3=12/u
-2u=36
u= -18 cm
now
focal length formula
1/f= 1/v - 1/u
1/f= 1/12 - 1/(-18) = 5/36
f=36/5
focal length of the lens= 7.2cm