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

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#### Let the focal lengths of the two lenses be f1 and f2.u1=OC1 andv1=I1C1u2=−C1I1 which is approximately equal to C2I1 and v2=C2I which is approximately equal to C1I∴1u1+1v1=1f1and 1u2+1v2=1f21OC1+1I1C1=1f1 and1−C1I1+1C1I=1f2So 1OC1+1I1C1=1f1+1f2=1F.Combined focal length of two thin lenses in contact is given by:F=f1f2f1+f2

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