Question

Two converging lenses with focal lengths of 40 cmand 20 cm are 16 cm apart. A 2.0 cm -tall object is 12 cm in front of the 40 cm -focal-length lens.

image postion was calculated to be 78 cm

Calculate the image height.

Answer 1

for 1st lens:
f = 40 cm
s = -12 cm
h = 2 cm
use:
1/f = 1/s' - 1/s
1/40 = 1/s'- 1/(-12)
1/s' = 1/40 - 1/12
s'= -17.14 cm
Magnification = h'/h = s'/s
h'/h = s'/s
h'/2 = -17.14/-12
h'= 2.86 cm

for 2nd lens:
f = 20 cm
s = -(17.14 + 16) = -33.14 cm
h = 2.86 cm
use:
1/f = 1/s' - 1/s
1/20 = 1/s'- 1/(-33.14)
1/s'= 1/20 - 1/33.14
s'=5.44 cm
Magnification = h'/h = s'/s
h'/h = s'/s
h'/2.86 = 5.44/-33.14
h'= -0.47 cm

Image position is 5.44 cm from 2nd lens
height is 0.47 cm