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

#### 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

1−C1I1+1C1I=1f2

So 1OC1+1I1C1=1f1+1f2=1F.

Combined focal length of two thin lenses in contact is given by:

F=f1f2f1+f2