When two lenses are used in combination, the first one forms an image that then

Question

When two lenses are used in combination, the first one forms an image that then serves as the object for the second lens. The magnification of the combination is the ratio of the height of the final image to the height of the object. A 1.10 cm -tall object is 58.0 cm to the left of a converging lens of focal length 40.0 cm . A second converging lens, this one having a focal length of 60.0 cm , is located 300 cm to the right of the first lens along the same optic axis.

A) Find the location and height of the image (call it I1) formed by the lens with a focal length of 40.0 cm .

B) I1 is now the object for the second lens. Find the location and height of the image produced by the second lens. This is the final image produced by the combination of lenses.

I have the answer for Part A: si = 129cm and hi = 2.44cm

Explanation / Answer

here,

height of object , ho = 1.1 cm

object distance , do = 58 cm

focal length , f1 = 40 cm

A)

di = 129 cm and hi = 2.44 cm ( given)

B)

distance between lens , d = 300 cm

object distance for lens2 , do2 = d - di = 171 cm

f2 = 60 cm

let the image distance be di

using the lens formula

1/f2 = 1/di2 + 1/do2

1/60 = 1/di2 + 1/171

di2 = 92.43 cm

the image height be h2

h2/hi = - di2/do2

h2 = 2.44 * 92.43/171

h2 = 1.32 cm

the height of image is 1.32 cm and the image distance is 92.43 cm

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