Question

Two identical diverging lenses are separated by 14 cm. The focal length of each lens is -9.5 cm. An object is located 3.9 cm to the left of the lens that is on the left. Determine the final image distance relative to the lens on the right

Answer 1

D = distance between two lens = 14 cm

for the left diverging lens :

f = - 9.5 cm

d_o = object distance = 3.9 cm

d_i = image distance = ?

using the lens equation

1/d_o + 1/d_i = 1/f

1/3.9 + 1/d_i = 1/(-9.5)

d_i = - 2.76 cm  

for the diverging lens on right

f = - 9.5 cm

d_o = object distance = 2.76 + 14 = 16.76 cm

d_i = image distance = ?

using the lens equation

1/d_o + 1/d_i = 1/f

1/16.76 + 1/d_i = 1/(-9.5)

d_i = - 6.06 cm

so the image is 6.06 on the left of right diverging lens