Physics 142
Laboratory 5
Geometric Optics
In this lab, you will explore the optics of thin lenses. A lens is a piece of refractive glass or plastic cut
into a particular shape so that it either spreads light rays out or brings them together.
Thin Lens Formulas
The primary equation governing the behavior of a thin lens is the thin lens equation:
"
"
"

œ
:
;
0
where
•
The variable : represents the distance from the object to the lens,
•
The variable ; represents the distance from the image to the lens, and
•
The constant 0 is the focal length of the lens.
When an object is very far away (i.e. : Ä _), the image distance will be equal to the focal length.
The magnification factor Q is defined as follows:
Q œ
size of image
size of object
The primary equation for Q is:
Q œ 
;
:
Sign Conventions
Positive
Negative
convex (converging) lens
concave (diverging) lens
object distance (:)
for any real object
for a virtual object
(i.e. an image from another lens)
image distance (; )
for a real image
(across the lens from the object)
for a virtual image
(on the same side as the object)
magnification (Q )
for an upright image
for an inverted (upside-down) image
focal length (0 )
A Convex Lens
We will be using a blank screen to detect images. We will start by using a distant object, and then
switch to using a light source with axes drawn.
Step 1: Measure the focal length.
Position your lens on the optical bench, pointing at some distant object (out a window for example).
Place the screen on the bench, and slide it back and forth until an image appears on the screen. Record
the positions of the lens and the screen, and subtract them to obtain the focal distance.
Step 2: The thin lens equation.
Now place an object (the light) at position !. Measure the diameter of the light. Place the lens some
distance away, and slide the screen until an image appears on it:
Record the following data:
1. The position of the lens.
2. The position of the image.
3. The diameter of the image.
Use the positions of the lens and the image to compute : and ; , and use the measured diameter to
compute Q . Repeat for 10–20 different positions of the lens.
Analysis
Include the following graphs in your lab write-up:
1. A graph of ; vs. :.
2. A graph of "Î; vs. "Î:.
3. A graph of Q vs. ;Î:.
Based on your data, does the lens obey the thin lens equation? Use your data to estimate the value of 0 .
Does this agree with the value of 0 that you observed? Also, does the observed magnification agree
with the equation Q œ ;Î:?
A Concave Lens
Next you will be exploring the image created by a concave lens. Unfortunately, the image formed by a
concave lens is always virtual (behind the lens), making it difficult to measure its position. Therefore,
you will be using a second lens to infer the position of the image.
The second lens will be convex (the same lens you used in the first part). The image from the first
lens acts as the object for the second lens. Since you already measured the focal length of the second
lens, you can use it to infer the position of the first image:
Specifically, consider the equation
"
:convex

"
;convex
œ
"
0convex
.
Since you know 0convex and you can measure ;convex , you can determine :convex . But then
;concave œ "&Þ! cm  :convex
Instructions
Place an object (the light) at position !. Place the concave lens some distance away, and place the
convex lens "&Þ! cm farther down. Always keep the convex lens 15.0 cm farther down than the
concave lens.
Slide the screen until an image appears, and record the positions of the lenses and the image. (Don't
worry about the diameter of the image). For each position, calculate :concave and ;concave Repeat for at
least 10–20 different positions of the lens.
Use your data to estimate the focal length of the concave lens.
Analysis
As with the convex lens, include graphs of ; vs. : and "Î; vs. "Î:. Does the concave lens obey the thin
lens equation? What is the focal length of the lens?