Two converging lenses (f1 = 9.00 cm and f2 = 6.00 cm) are separated by 18.0 cm.

Question

Two converging lenses (f1 = 9.00 cm and f2 = 6.00 cm) are separated by 18.0 cm. The lens on the left has the longer focal length. An object stands 12.0 cm to the left of the left-hand lens in the combination. a) Graphically locate the image. Use a full sheet of paper and draw to scale. Use a ruler! b) Calculate the final image distance relative to the lens on the right. c) Calculate the overall magnification. d) Is the final image real or virtual? e) Is the final image upright or inverted? f) Is the final image larger or smaller?

Explanation / Answer

ens formula and magnification

1/v -1/u = 1/f and m = v/u

v=> image distance and u for objecct now

f1 = +9 and f2 = +6 , d= 18 cm

u = -12   

locate the image formed by lense 1

1/v-1/ -12 = 1/ 9

v1= 36

m1 = v /u = 36/ -9 = - 4 inverted real

now this image will work as object for second lense

distance from second lens from this image = 36- 18 = 18 cm

u = -18   

now find the image

1/ v- 1/ -18 = 1/ 6

v = 9 cm this real image inverted

m = v/u = 9/ -6 = -1.5

so final image will be upright and real image and distance from right lense = 9 cm

total megnification = -4*-1.5 = 6 it wll be large   

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