Find the Focal Length of the Lens
A differentiated lab to test you skill
with lab reports and geometric optics
Ray Tracing for Lenses
Lenses are used to focus light and form images. There are a variety of possible types; we
will consider only the symmetric ones, the double concave and the double convex.
Ray Tracing for Lenses
If we think of a convex lens as consisting of prisms, we can see how light going
through it converges at a focal point (assuming the lens is properly shaped).
Ray Tracing for Lenses
A concave lens can also be modeled by prisms:
Ray Tracing for Lenses
These diagrams show the principal rays for both types of lenses:
The three principal rays for lenses are similar to those for mirrors:
• The P ray—or parallel ray—approaches the lens parallel to its axis.
• The F ray is drawn toward (concave) or through (convex) the focal point.
• The midpoint ray (M ray) goes through the middle of the lens. Assuming the lens is
thin enough, it will not be deflected. This is the thin-lens approximation.
Ray Tracing for Lenses
The convex lens forms different image types depending on where the object is
located with respect to the focal point:
The Thin-Lens Equation
We derive the thin-lens equation in the same
way we did the mirror equation, using these
diagrams:
The Thin-Lens Equation
Sign conventions for thin lenses:
The focal Length can be found…
• Using the equations seen yesterday, your single
objective is to find the focal length of the convex
lens that is in your group’s optics kit.
– The way you communicate your findings will dictate
your grade. There are several options to choose from.
The ‘D’ Option
• This option will earn you up to a ‘D’ or 69%
• You provide an answer for the focal length
with the measurements and math. Minimal to
no commentary on procedure and analysis.
f = 15.0cm
The ‘C’ Option
• This option will earn you up to a ‘C’ or 79%
• You provide an answer for the focal length
with the measurements and math. A clear and
concise commentary is given on the procedure
and analysis used.
The ‘B’ Option
• This option will earn you up to a ‘B’ or 89%
• You provide an answer for the focal length
with the measurements and math. A clear and
concise commentary is given on the procedure
and analysis used. More than one pair of
object and image distances are used to
calculate the focal length.
Trial #
1
2
3
do
di
f
The ‘A’ Option
• This option will earn you up to an ‘A’
or 100%
• You provide an answer for the focal
length with the measurements and
math. A clear and concise
commentary is given on the
procedure and analysis used. More
than one pair of object and image
distances are used to calculate the
focal length. A graph of the data is
shown to depict how the focal
length can be visualized as the slope
of a function relating di and do.
The Options for the Lab
• Your single objective is to
find the focal length of
the convex lens that is in
your group’s kit.
• All of the levels allow you
to do this, and they all
build on each other.
– Ex: In order to do the Blevel, you must be able to
do the C-level work
• Add a ray-diagram to any
level for a polished look!
The options for this lab
D –Level
C-level
Find an answer for
the focal length of
your convex lens
Find a focal length
and explain how you
obtained it.
B-Level
A-Level
Use multiple data
points to minimize
error in your focal
point value.
Use multiple data
points and graphical
analysis to minimize
errors in results.