Question

A converging lens (f₁ = 12.7 cm) is located 30.6 cm to the left of a diverging lens (f₂ = -6.48 cm). A postage stamp is placed 33.9 cm to the left of the converging lens. Locate the final image of the stamp relative to the diverging lens.

Answer 1

for converging lens :

f₁ = 12.7 cm

d_o1 = 33.9 cm

d_i1 = ?

using the lens equation

1/d_i1 + 1/d_o1 = 1/f₁

1/d_i1 + 1/33.9 = 1/12.7

d_i1 = 20.3 cm

for diverging lens :

D = distance between the lens = 30.6 cm

d_o2 = object distance for diverging lens = D - d_i1 = 30.6 - 20.3 = 10.3 cm

f₂ = - 6.48 cm

d_i2 = image distance for diverging lens = ?

using the lens

1/d_o2 + 1/d_i2 = 1/f₂

1/10.3 + 1/d_i2 = 1/(-6.48)

d_i2 = - 4 cm

image is 4 cm to the left of diverging lens