Lecture 6: Thin Lens Combinations
Lecture aims to explain:
1. Ray tracing diagrams for two thin lenses
2. Image forming for multiple lens combinations
3. Doublet lens
Ray tracing diagrams for two thin
lenses
L1
L2
First construct the image formed by
L1 alone using rays 1 and 3.
1
S1
Fi2
Fo1
3 Fo2
O1
O2
f2
d
f1
so1
P1’
2
so2
si1
L1
L2
Fi1
3
Fo1
Fi1
Fo2
O1
Fi2
Ray 2 is constructed by running
backward from P1’ through O2. The
insertion of L2 has no effect on ray 2.
2
O2
Ray 3 is refracted through the image
focus Fi2
Image forming for multiple lens
combinations
Analytical treatment for two thin lenses
L1
L2
1
S
1
Fi2
Fo1
3 Fo2 O1
f1
so1
f2
d
O2 Fi1
2
P1’
so2
si1
Image will be formed at a
distance si2 from the second lens:
f 2 d − f 2 s o1 f1 /( s o1 − f1 )
si 2 =
d − f 2 − s o1 f1 /( s o1 − f1 )
We apply the rule for image
forming by a system of lenses
the image produced by the
first lens plays the role of the
object for the second lens
The total magnification of
the two lens system is given
by M=M1M2
Doublet lenses
Doublet lenses
For doublet lenses d=0
effective focal length
of a doublet lens
1 1
1
=
+
f
f1 f 2
Example 6.1
A pair of convex lenses with focal lengths f1=5 cm and f2=7cm are
separated by d=15 cm. If a 2 cm tall object is placed 10 cm from the first
lens (with focal length f1) what is the position of the final image and what is
its magnification. Is that a real or virtual image?
Example 6.2
A concave lens with a focal length f1=-5 cm is positioned at a distance d
behind a convex lens with a focal length f2=15cm. A beam of light parallel
to the optical axis of the lens system is incident on the convex lens. Find
the range of separations d for which the system of these two lenses will
focus this beam into a point.
Example 6.3
Find magnification of a system of two convex lenses imaging an object
placed in the focal plane of one of the lenses.
Example 6.4
Find the effective focal length of a system of 10 lenses each having a
focal length f and negligible separation from the neighbouring lenses.
SUMMARY
Rules for ray tracing diagrams for compound lenses
have been considered
Image forming by a compound lens relies on the rule
that the image produced by the first lens plays the
role of the object for the second lens
The total magnification of the two
lens system is given by M=M1M2
effective focal length
of a doublet lens
1 1
1
=
+
f
f1 f 2