Two converging lenses having focal lengths of f1 = 11.0 cm and f2 = 18.5 cm are

Question

Two converging lenses having focal lengths of f1 = 11.0 cm and f2 = 18.5 cm are placed a distance d = 48.5 cm apart as shown in the figure below. The image due to light passing through both lenses is to be located between the lenses at the position x = 32.5 cm indicated. (a) At what value of p should the object be positioned to the left of the first lens? cm (b) What is the magnification of the final image? (c) Is the final image upright or inverted? inverted upright (d) Is the final image real or virtual? real virtual

Explanation / Answer

for lens 2

image distance s2' = -(d-x) = -(48.5-32.5) = -16 cm

object distance s2 =?

focal length f2 = 18.5 cm

1/s2 + 1/s2' = 1/f2

1/s2 - 1/16 = 1/18.5

object distance s2 = 8.5 cm

this object distance is the image distance for lens 1

s1' = d - s2 = 48.5 - 8.5 = 40 cm

for lens 1

object distance s1 = p

image distance s1' = 40 cm

focal length f1 = 11 cm

1/s1 + 1/s1' = 1/f1

1/p + 1/40 = 1/11

object distance p = 15.2 cm <<<<-------ANSWER

(b) magnification M = M1*M2 = (s1'/s1) *(s2'/s2)

M = (40/15.2)*(-16/8.5)

M = -4.93 <<<--------ANSWER

M = 4.93 <<<--------ANSWER

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(c)

upright

====================

d)

final image is virtual

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