A small object is 250 cm from a diverging lens as shown in t

A small object is 25.0 cm from a diverging lens as shown in the figure(Figure 1) . A converging lens with a focal length of 12.2 cm is 30.0 cm to the right of the diverging lens. The two-lens system forms a real inverted image 17.0 cm to the right of the converging lens.What is the focal length of the diverging lens?

Solution

1 / d_o2 + 1 / d_i2 = 1 / f₂

1 / d_o2 = 1 / 12.2 - 1 / 17

d_o2 = 43.21 cm

d_i1 = 30 - 43.21 = -13.21 cm

For diverging lens

1 / d_o1 + 1 / d_i1 = 1 / f₁

1 / f = 1 / 25 - 1 / 13.21

f₁ = -28 cm