Question

A 2.5-cm-tall object is 30 cm to the left of a lens with a focal length of 15 cm . A second lens with a focal length of 48 cm is 62 cm to the right of the first lens.

Calculate the distance between the final image and the second lens.

Calculate the image height.

Answer 1

For the first lens :

f = 15 cm

do = object distance = 30 cm

di = image distance = ?

ho = object height = 2.5 cm

Using the lens equation

1/do + 1/di = 1/f

1/30 + 1/di = 1/15

di = 30 cm

hi = image height

using the equation

hi/ho = - di/do

hi/2.5 = - 30/30

hi = - 2.5 cm

For the second lens :

f = 48 cm

do = object distance = 60 - 30 = 30 cm

di = image distance = ?

ho = object height = 2.5 cm

Using the lens equation

1/do + 1/di = 1/f

1/30 + 1/di = 1/48

di = - 80 cm

So final image is 80 cm.

hi = image height

using the equation

hi/ho = - di/do

hi/2.5 = - (- 80)/30

hi = 6.67 cm

Image height is given as 6.67 cm