Two converging lenses having focal lengths of f_1 = 12.5 cm and f_2 = 22.0 cm ar

Question

Two converging lenses having focal lengths of f_1 = 12.5 cm and f_2 = 22.0 cm are placed a distance d = 51.5 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 = 31.5 cm indicated. At what value of p should the object be positioned to the left of the first lens cm What is the magnification of the final image Is the final image upright or inverted inverted upright Is the final image real or virtual real virtual

Explanation / Answer

for converging lens f2

image distance q2 = (d-x) = 51.5-31.5 = -20 cm

object distance p2 = ?

focal lengh f2 = 22 cm

1/p2 + 1/q2 = 1/f2

1/p2 - 1/20 = 1/22

object distance p2 = 10.5 cm

magnification m2 = -q2/p2 = 20/10.5 = 1.9

for converging lens f1

image distance q1 = d - p1 = 51.5-10.5 = 41

object distance p1 = p

focal length f1 = 12.5 cm

1/p1 + 1/q1 = 1/f1

1/p + 1/41 = 1/12.5

p = 18 cm

magnification m1 = -41/18 = -2.28

(a)

p = 13.15 cm

(b)

overall magnification M = m1*m2 = -1.9*2.28 = -4.33

(c)

inverted

(d)

virtual

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