SPH3U Physics Optics Unit
A Diverging Lens Experiment that WORKS!
Problem to Address:
Students who conduct experiments with diverging lenses can get very frustrated; images of objects are virtual
which cannot be projected onto a screen and their position is very hard to determine experimentally.
Objective:
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The objective of this experiment is to measure the focal length of a diverging lens .
Theory:
Light refracts when passing between media with different indices of refraction (n) and this property can be
utilized to bend light in useful ways. A converging lens, seen in Figure 1, can be used to focus parallel light rays
and form a real image as the light travels from air (n=1.00) to glass (n=1.50) and back to air. When light rays,
traveling parallel to the principal axis of the lens, are refracted they cross at a point called the focus.
f
f
Figure 1 –Focal length of a converging lens
Figure 2 – Focal length of a diverging lens
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An important property of a lens is its focal length , f. The focal length of a thin lens, derived from simple
geometry, is the distance from the optical centre of the lens to the focal point, and is given by the equation (thin
lens equation - TLE):
1
1
1


f di do
where do is the object distance and di is the image distance from the lens.
Laboratory experiments using converging lenses (focal length is positive) allow students to readily correlate their
experimental data with values found using the thin lens equation.
However, the principal focus of a diverging lens, (Figure 2), is virtual (f is negative) and for all positions of an
object, the image formed is virtual, upright, and smaller. The image is always located between the principal
focus and the optical centre of the lens on the same side of lens as the object, and as the image is virtual, it
cannot be projected onto a screen.
Object
Principal Focus
(virtual)
Image
Figure 3 - Viewing virtual image of diverging lens
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Original idea for the experiment was found on the University of Idaho Physics department website,
http://www.phys.uidaho.edu.
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The focal length is a function of the index of refraction of the lens material and the radii of curvature R1 and R2 of the two
lens faces.
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PED4126 Physics-Senior
Giles, Jones, Parent, Sweeney
SPH3U Physics Optics Unit
A Diverging Lens Experiment that WORKS!
When experimenting with diverging lenses (Figure 3) the image can be seen but its position is hard to
determine. (It may be possible to see the “image” of the object on the object-facing side of the diverging lens if
that side is slightly reflective. The image is the same as that formed by a concave mirror with the same focal
length.)
The Experiment - Measure the focal length of a diverging lens:
Step 1: To determine the focal length of a diverging lens we need to form a virtual object for the diverging lens.
This can be done by making real image of the object with a converging lens. Figure 4 shows how the real
image (virtual object) is formed.
Image
Object
Screen
Converging
Lens
di
do
Figure 4 – Creating the virtual object with a converging lens
The distance of the image (di) from the converging lens can be found through focusing the image onto a screen.
The focal length of the converging lens can be verified using the TLE knowing the object distance (do) and
image distance (di).
Step 2: Add the diverging lens between the converging lens and its image, some distance (d) from the
converging lens - Figure 5. The new real image is formed further from the converging lens. Adjust the position of
the screen and diverging lens to form a clear image. The position of the real image formed (dR) is recorded.
Diverging
Lens
do
d
dV
dR
Figure 5 – Add the diverging lens
Step 3: Determine the position of the diverging lens’ virtual object. This is the distance of virtual object (dv) from
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the diverging lens and is calculated by dV = (d – di); Note that dV is negative .
Step 4: Use the TLE, with dV and dR, to determine the focal length (fd) of the diverging lens.
Step 5: Move the main object, and/or converging lens position and repeat steps 1-4. Average and present the
results.
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Sign conventions for images and objects: The object distance is positive if the object is on the incoming side of the lens
(object is “real”), and negative if the object is on the outgoing side (object is “virtual”). Image distance is positive if the
image is on the outgoing side of the lens (image is “real”), and negative if the image is on the incoming side (image is
“virtual”). Another way to think of sign conventions is to consider the left side of the lens as object space and the right side
image space. An image or (virtual) object in the “wrong” space will have a negative distance. Hence, dV is negative.
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PED4126 Physics-Senior
Giles, Jones, Parent, Sweeney
SPH3U Physics Optics Unit
A Diverging Lens Experiment that WORKS!
EXPERIMENTAL WORKSHEET
Trial 1
Form real image with a converging lens.
The real image becomes the virtual object for
the diverging lens.
Step 1
Image
Object
di 
di 
do 
do 
Screen
Converging
Lens
fc 
di
do
Trial 2
d o d i 

d o  d i 
fc 
d o d i 

d o  d i 
Measure image distance (di), object distance
(do) and record given focal length (fc) of
converging lens. Check value found for fc with
TLE.
Step 2
Add the diverging lens.
Place the lens between the converging lens
and its image.
Diverging
Lens
do
d
dV
Step 3
Step 4
Step 5
dR 
d
d
d v  d  d i  
d v  d  d i  
dR
Adjust the position of the diverging lens and
the screen to obtain a clear image. Measure
image distance (dR) and distance between
lenses (d).
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dR 
Determine the position of the diverging lens’
virtual object (dV)
Calculate focal length of diverging lens.
Using the TLE with dV and dR, find the focal
length (fd) of the diverging lens.
Alter position of object and/or converging lens
and repeat Steps 1-4. Average and present
results.
fd 
d v d R 

d v  d R 
fd 
d v d R 

d v  d R 
Focal length (fd) =
PED4126 Physics-Senior
Giles, Jones, Parent, Sweeney