Question

A 1.5-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 -7 cm is 47 cm to the right of the first lens.

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

B) Calculate the image height.

Answer 1

Image distance for 1st lens

By using lens formula

1/v - 1/u = 1/f

1/v - 1/(-30) = 1/15

v = 30 cm

This image acts object for 2nd lens

So object distance for 2nd lens = 47 - 30 = 17 cm

So by using lens formula

1/v - 1/u = 1/f

1/v - 1/(-17) = 1/(-7)

v = - 4.96 cm

A)

Distance between final image and 2nd lens = 4.96 cm

B)

1st image height

By magnification m = hi/ho = v/u

hi/1.5 = 30/(-30)

hi = - 1.5 cm

Final image height

By magnification for 2nd lens

m = hi/ho = v/u

hi/(-1.5) = - 4.96/(-17)

hi = - 0.44 cm