Two thin lenses in contact
In many optical instruments there may be
compound lenses, that is, two or more lenses in contact. We will first deal with the case of
two thin lenses in contact.
In Figure 1, let the be focal lengths of the two
lenses be f
1 and f
2.
u
1 = OC
1 and v
1 =
I
1C
1u
2= -C
1I
1 which is approximately equal to C
2 I
1
and v
2 = C
2I which is approximately equal to C
1I
Therefore
1/u
1 +
1/v
1 = 1/f
1 and 1/u
2 + 1/v
2 =
1/f
21/OC
1 + 1/I
1C
1 = 1/f
1 and 1/-
C
1I
1 + 1/C
1I = 1/f
2Therefore:
1/OC
1 +
1/I
1C
1 = 1/f
1 + 1/f
2 = 1/F
Combined focal length
of two thin lenses in contact is given by:
where F is the focal length of the
combination.
The combined focal length for two thin lenses separated by a distance
a (Figure 2) is given by the equation:
