Lecture 8: Image forming using thin lenses
Lecture aims to explain:
1. Ray tracing diagrams for thin lenses
2. Fine image forming
3. Sign Conventions
4. Lateral Magnification
5. System of two lenses
Ray tracing diagrams for thin lenses
Rules for ray tracing diagrams
(1) A ray passing through the centre of a lens is not affected
(2) A ray directed parallel to the optical axis passes through a
focal point
(3) A ray directed toward, or away from, a focal point emerges
parallel to the optical axis
example for a
convex lens
2
Any two principal rays are
sufficient for locating the
image produced by a lens
1
3
Image forming by convex and
concave lenses
Real and virtual images
Example: Convex lens, real image
Also use the Thin Lens Eq.
Example: Concave lens, virtual image
Sign conventions
Main sign rules
Sign Conventions: for thin lenses
with light entering from the left:
so
fo
si
fi
yo,yi
It follows that so negative for a
virtual object and si negative
for a virtual image
+ left of the lens
+ if Fo left of the lens
+ right of the lens
+ if Fi right of the lens
+ above the optical axis
yo
Fi
Fo
yi
f
so
f
si
Lateral magnification
Lateral magnification
As follows from geometrical
considerations of the figure:
yi
si
M=
=−
yo
so
yo
Fi
Fo
yi
f
so
f
si
Rules for ray tracing diagrams for two 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
Ray 2 is constructed by
running backward from P1’
through O2. The insertion of
L2 has no effect on ray 2.
si1
L1
L2
Fi1
3
Fo1
Fi1
Fo2
O1
O2
Fi2
2
Ray 3 is refracted through the
image focus Fi2
Rule for analytical treatment for two thin lenses
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
Example 8.1
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 8.2
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 8.3
Find magnification of a system of two convex lenses imaging an object
placed in the focal plane of one of the lenses.
SUMMARY
See Hecht Optics pp 159-170
Rules for ray tracing diagrams
(and image forming):
(1) A ray passing through the
centre of a lens is undeviated
(2) A ray directed parallel to the
axis passes through a focal point
(3) A ray directed toward, or
away from, a focal point
emerges parallel to the axis
Sign Conventions: for thin
lenses with light entering
from the left:
so + left of the lens
fo + if Fo left of the lens
si + right of the lens
+ if Fi right of the lens
fi
yo,yi + above the optical axis
Both images and objects can be real or virtual
Lateral magnification is positive
(negative) for an erect (inverted) image
System of thin lenses: the image
produced by the first lens plays the
role of the object for the second lens
yi
si
MT =
=−
yo
so
The total magnification
of the two lens system is
given by M=M1M2