Two converging lenses with focal lengths of 40 cm and 20 cm

Two converging lenses with focal lengths of 40 cm and 20 cm are 10 cm apart. A 2 cm tall object is 15 cm in front of the 40 cm focal length lens. What is the position and height of the image?

Solution

Here,

f1 = 40 cm

f2 = 20 cm

d = 10 cm

hi = 2 cm

object distance , do1 = 15 cm

using lens formula

1/40 = 1/15 + 1/di1

di1 = -24 cm

for the second lens

do2 = 24 + 10 = 34 cm

Using lens formula

1/20 = 1/34 + 1/di2

di2 = 48.6 cm

the position of the final image is 48.6 cm

for height of image hi

hi = (48.6/34) * (24/15) * 2

hi = 4.57 cm

the height of image is 4.57 cm