By definition, the magnification is m = hi/**. In this case, since the image is inverted, the image height is negative. Thus,
m = −1.5/3.5 = −0.42857
The magnification tells us something about the image and object distances according to m = −di/do. Thus,
(−0.42857) = − di/do
Since we know the image distance, we can calculate the object distance:
(−0.42857) = − 13/do ⇒ do = 30.333
We can now use the lens equation (1/do + 1/di = 1/f) to calculate the focal length:
1/(30.333) + 1/13 = 1/f ⇒ f = 9.1000
