Question

An object is 20 cm in front of a diverging lens that has a focal length of -13 cm. How far an front of the lens should the object be placed so that the size of the image is reduced by a factor of 1.8? Number Units

Answer 1

given
object distance d0 = 20cm
focal length f = -13cm
size of the image is reduced by 1.8

we know that
1/do +1/di =1/f
1/20 +1/di = -1/13
di = -7.8 cm
magnification M = -di / do = 7.8/20 = 0.39

(1/1.8)*M = (1/1.8)*0.39
M =0.216
0.216=7.8/do
do =36.11 cm

Answer 2

This will not lead to a correct solution.