Question

A 1.8-cm-tall object is 28cm  to the left of a lens with a focal length of 14cm . A second lens with a focal length of -6cm  is 39cm  to the right of the first lens.

Part A:

Calculate the distance between the image and the second lens.

Part B:

Calculate the image height.

Please show how you obtained the answers!

Answer 1

shown above

The focal length of the first lens f1 = 14 CM

The object distance is u = 28 cm

the height of the the object is h = 1.8 cm

The image of this lens formed at

1/f =1/u +1/v

1/14 = 1/28 + 1/v

v =28 cm (image is real)

The height of the image is h' = mh

Where magnification m = -v/u

m = -28/28= -1 (image is inverted)

The height of the image is h' = 1.8cm

The focal length of the other lens is f2 = -6 cm

The image of the first lens as an object to the second as it is placed at 11 cm on the right of the lens

object distance u' = 11 cm

The image will be formed at

1/f = 1/u + 1/v

1/-6 = 1/11 +1/v

v = -3.88 cm (image is virtual)

The distance between the image and the second lens is 3.88 cm

image height h'' = m'h'

m' is the magnification of the second lens

m' = -v/u

m' = 3.88/11

m' = 0.3527 (the image is diminished and up right)

The image height h'' = 0.3527*1.8 cm

h'' = 0.634 cm

The image height is 0.634 cm