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Question

In the situation shown in the figure, three lenses of focal lengths 20 cm, 30 cm and 36 cm are held coaxial such that separation between first and second lens is 12 cm and between second and third lens is 10 cm. If the final image of an object at a distance of 30 cm from first lens is at a distance 10x cm from the middle lens, then find the value of x.

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Solution

For the lens
u=30 cm ; f=20 cm
1v=120130v=60 cm
For second lens
u=+48 cm ; f=30 cm
1v=130+148=16+10480=6480
v=80 cm
For third lens
u=90 cm ; f=36 cm
1v=136190=104360=6360
v=60 cm
From middle lens, position of final image is 70 cm
10x=70
x=7

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