Question

Drive an expression for equivalent focal length of two thin lenses kept in contact.

Solution
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Let the focal lengths of the two lenses be f1 and f2.
u1=OC1 and
v1=I1C1
u2=C1I1 which is approximately equal to C2I1 and
v2=C2I which is approximately equal to C1I
1u1+1v1=1f1
and 1u2+1v2=1f2
1OC1+1I1C1=1f1 and
1C1I1+1C1I=1f2
So 1OC1+1I1C1=1f1+1f2=1F.
Combined focal length of two thin lenses in contact is given by:
F=f1f2f1+f2
659011_623393_ans_8b78deea294a48609dc84fb7b925283d.png

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