Two converging lenses having focal lengths of f_1 = 12.0 cm and f_2 = 20.5 cm ar

Question

Two converging lenses having focal lengths of f_1 = 12.0 cm and f_2 = 20.5 cm are placed a distance d = 50.5 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 = 30.0 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 f2:

image distance, di2 = - (50.5 - 30) = - 20.5 cm

f2 = 20.5 cm

applying lens equation,

1/f2 = 1/do2 + 1/di2

1/20.5 = 1/do2 + 1/(-20.5)

do2 = 10.25 cm from f2 in between f1 and f2:

do2 is object for f2 but image of f1.

di1 = 50.5 - 10.25 =40.25 cm

f1 = 12 cm

1/f1 = 1/di1 + 1/do1

1/12 = 1/40.24 + 1/do1

do1 = 17.1 cm

p = 17.1 cm ........Ans(a)

(b) m = m1 m2

m1 = -40.24 / 17.1 = -2.35

m2 = -(-20.5)/ 10.25 = 2

m = - 4.7

(c) m is -ve hence final image will be inverted.

(d) final image is virtual.

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