Thin Lenses
Dr. Timothy Niiler, WCU
Based on Laboratory by Dr. Matt Waite
Introduction
The thin lens equation is a good approximation for the determination of image or object distances
given the focal length of a lens. The equation presumes that the lens involved is thin enough that
only a single diffraction takes place and that the incoming rays of light from the object are
roughly paraxial. This equation is stated as:
1)
1 1 1
 =
d0 di f
where do is the object distance, di is the image distance, and f is the focal length of the lens. For
a convex lens, f is always positive. In this lab, we will be validating equation 1) for a convex
(converging) and a concave (diverging) lens by making a series of measurements in which the
object and image distances vary.
Procedures
Part 1
Setup the optical bench as shown below.
You will need the light source, three mounting brackets, a convex lens (f=127mm), an object
arrow, and a screen. Mount the object arrow at A (at 0mm to simplify your life), the lens at L and
the screen at S. Note that these slides have offsets which must be considered:
Arrow - 4.5 mm
Lens - 6.5 mm
Screen - 4.5 mm
If, for example, the white line on the mounting bracket holding the lens lined up with the 100.0
mm mark on the optical bench, you would add 6.5 mm to 100 to get the true position of the lens
(106.5mm). Be certain to do this for the arrow and screen as well. Note that if your slide is on
the front side of the mounting bracket, you will subtract the offset instead of adding it.
Start by placing the lens (L) at about the 600 mm mark and then move the screen (S) until the
image is in focus. Record the positions of L and S in the table below. Now move the lens 5 cm,
closer to the object arrow and repeat. Keep moving the lens closer to the arrow in steps of about
5 cm until the image becomes very large and can no longer be focused on the screen. For each
position of the lens, record the value of the object distance (do= L - A) and the image distance
(di = S – L). Record your values in the table below.
Table 1: Determination of Focal Length of Convex Lens (be certain to include uncertainties
in measured quantities).
Trial
Distance to
Lens
Distance to
Screen
L
S
do
di
1
2
3
4
5
6
7
8
9
10
Analysis (Part I)
Make a graph of 1/di versus 1/do where do is the object distance and di is the image distance.
From this graph, estimate the focal length of the lens. Be certain to include any needed
annotations on the graph (including units!). Overplot what is expected theoretically by
calculating 1/di from the thin lens equation using the known focal length of the lens.
Theoretically, what should the slope of your data be if your data were perfect. Why (justify this)?
Explain why, physically, the x- and y-intercepts of your should be nearly equal to each other.
How do the x- and y- intercepts relate to the focal length of your lens? How does this relate to
the uncertainty in your derived focal length? Based on comparison of your theoretical overplot
with your actual data, does your data support the thin lens equation? Explain any anomalies you
might have encountered. Is the given focal length of the lens the same as your experimentally
derived focal length within your margin of error?
Part 2 (Procedures and Analysis)
Next, mount your laser in place of the light
source. Remove the object arrow, if mounted
separately from the light source. Replace the
convex lens with the concave lens. In this case,
we are using the laser because, to first order, it
provides parallel, collimated light which will
follow a path as traced out in the diagram at
right.
Using similar triangles, it can be shown that:
2)
ho
hi
=
f f di
and from this equation, the focal length, f, can be determined. The quantities ho and hi can be
determined by measuring the width of the laser beam before it passes through the lens and
afterwards, respectively.
In this portion of the lab, it is up to you to design the experiment such that you get the most
accurate value for the focal length. Do not ask your instructor to tell you what to do. Some
issues to consider are whether or not the light from the laser is truly parallel, is your precision
likely to be greater with larger or smaller di and hi? Does the distance between the laser and the
lens matter? If so why? If not, why not. Be specific. Make as many measurements as you need
to back up your arguments, and do not forget to propagate error! Do your results validate the
thin lens equation?