A lens with an unknown focal length forms an image of an object that is 12 cm away from the lens,inverted,and a factor of 3.0 larger in size than the object.Where is the object located?
A)4.0 cm from the lens on the same side of the lens as the image
B)4.0 cm from the lens on the other side of the lens from the image
C)36 cm from the lens on the same side of the lens as the image
D)36 cm from the lens on the other side of the lens from the image
E)No object could have formed this image.

Question

Quizplus · Accepted Answer

Using the magnification formula: 
m = -v/u = 3.0
where v is the image distance and u is the object distance. Since the image is inverted, m is negative.
Using the lens formula:
1/f = 1/v - 1/u
We can substitute 3v for u (since the magnification is 3), and we know that the focal length of the lens is positive (since it forms a real image):
1/f = 1/v - 1/3v = (3 - 1)/3v = 2/3v
Solving for v:
v = 3/2f
Substituting this into the magnification formula:
-3/2 = v/u = 3.0
u = -2.0 cm
Since u is negative, the object must be on the opposite side of the lens from the image, so the answer is B.

A Lens with an Unknown Focal Length Forms an Image