Question

A converging lens with focal length of 30 cm and a diverging lens with focal length of 10 cm are 15 cm apart. A 4-cm-tall object is 10 cm in front of the 30-cm-focal-length lens. Use ray tracing to find the height of the image in cm

Answer 1

for the converging lens :

f = 30 cm

d_o = object distance = 10 cm

d_i = image distance = ?

Using the equation

1/d_o + 1/d_i = 1/f

1/10 + 1/d_i = 1/30

d_i = - 15 cm

h_o = object height = 4 cm

h_i = image height = ?

Using the equation

h_i/h_o = - d_i/d_o

h_i/4 = - (- 15)/10

h_i = 6 cm

for the diverging lens :

f = - 10 cm

d_o = object distance = 30 cm

d_i = image distance = ?

Using the equation

1/d_o + 1/d_i = 1/f

1/30 + 1/d_i = - 1/10

d_i = - 7.5 cm

h_o = object height = 6 cm

h_i = image height = ?

Using the equation

h_i/h_o = - d_i/d_o

h_i/6 = - (- 7.5)/30

h_i = 1.5 cm