Thin Lenses – pts 1&2 – General
documentation
Deliverable
Group summary
Equipment needed
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Pasco light boxes
Thin paper
Convex and concave lenses
Ruler
Estimated Time needed for the activity
30 minutes max
Pre-lab questions
1. Explain why a ray that passes through the center of a lens has the same exit angle as the
angle of incidence.
2. Describe a simple method for determining the approximate focal length of a converging
lens by using a distant light source. Use the thin lens equation to justify this method.
3. Predict which color light will have the shorter image distance, red or blue.
4. Summarize the cause of spherical aberrations and what can be done to improve images.
5. Summarize the cause of chromatic aberrations and what can be done to improve images.
Pre-lab answers
1. Explain why a ray that passes through the center of a lens has the same exit angle as the
angle of incidence.
Since rays passing through the top or bottom half of a convex lens bend toward the central axis,
a ray passing through the center does not change its direction.
2. Describe a simple method for determining the approximate focal length of a converging
lens by using a distant light source. Use the thin lens equation to justify this method.
If you set your source to be at nearly infinity, the image distance will be the focal length of the
converging lens. Using the thin lens equation, this means, 1/do ~ 0 so that f ~ di.
3. Predict which color light will have the shorter image distance, red or blue.
“Blue bends better,” so blue should have a shorter image distance.
4. Summarize the cause of spherical aberrations and what can be done to improve images.
Spherical aberration is caused by an increased refraction of light when near the edge of a lens –
to the point that the thin lens approximation breaks down and the rays are focused at a different
point depending on radius (causing a blurry image). To counteract this effect, use a mask or
aperture to only use the central part of the lens.
5. Summarize the cause of chromatic aberrations and what can be done to improve images.
Chromatic aberrations are caused by the fact that materials have an index of refraction that is
frequency dependent. This means that the refraction will depend on the color of light and all
energies will not focus in the same spot, causing a blurry image. To counteract this effect, use a
narrow spectrum of light.
Pre-lab discussion points
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Stress that the lab is being split over two days and the students should focus on doing
whatever needs to be done in the dark first, analysis can be done after the fact once we
turn on the lights.
We’re starting with ray tracing – this starts out as a memorization issue for students but
hopefully they will start to think about it in terms of a derivation like any other equation
we’ve covered in the class .
There are three people per group, so each one should take a turn drawing one principle
ray.
The second part of the lab doesn’t need to take much time – students may try to be
overly precise with the distance measurements. They really just need three quick points
to find focal lengths.
Teaching Tips/pointers for doing lab
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The first part of the lab is doing a virtual image’s ray tracing – the idea of tracing back
(convention is to use dotted lines) will seem strange to a few groups – just make sure
they get a chance to finish one image all the way through.
Watch that students are directing the light source through the tip of the “object” –
arrow head – that they’ve drawn so they get a good image.
Encourage students to play with the aperture – what happens if half of the object is
covered?
Post-lab discussion questions
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General discussion about eyeglasses (time permitted) or some other optics example –
use of lenses in a daily/real life setting.
An interesting different example might be to talk about different types of telescope
designs (refractors vs reflectors) and what other considerations go into the particular
designs (which doesn’t even touch on wavelength dependence of designs)…
Extension Problems
1. Simulation for this
Solutions for Extension Problems
Rubric for grading Deliverable
Names:__________KEY________________________________________ Group:_______________
Optics Lab: Thin Lenses (over 2 days) (35pts) (+15 pts for pre-lab)
Part 1: Ray Tracing (8 pts)
What is the height of your image? (1pt) Recorded value (will vary) PLUS uncertainty
Is it reduced or larger than the original object? (1pt)
Upright or inverted? (1pt) Inverted Final magnification? (1pt) Will vary PLUS uncertainty
Is this what you expected? Any general comments about the ray tracing? (1pt) Lots of possible
summaries here – be lenient with the 1 pt.
Can you use the simulation linked in the lab writeup to build a microscope or a telescope?
What designs/arrangements work best to magnify? (3pts) Yes, you can use the simulation to
build a microscope and a telescope. Good answers will give specific examples or even a screen
shot of a lens assembly design.
Part 2: Optic Bench Work (15pts)
Convex lens: (labeled focal length: f =_____________) (1 pt – value) (5 pts for chart)
do
u do
di
u di
f
uf
Find the average f and its uncertainty. Compare this to the actual focal length of your lens.
(1pt) Average, (1pt) Uncertainty, (1pt) comparison
Qualitatively describe what happens when do approaches f. (1 pt)
As do approaches f, di approaches infinity (it becomes nearly impossible to focus the image)
Effects of filters (step 8): Initial do =_______±________ and di =_______±________
(1 pt for recorded values)
What effects does the BLUE filter have on your image? Is the image sharper with or without
the filter? Does the image distance increase or decrease? (2pts) The image distance should
decrease and the image might be sharper (definitely dimmer) with only one color.
What effects does the RED filter have on your image? Is the image sharper with or without the
filter? Does the image distance increase or decrease? (2pts) The image distance should
increase and the image might be sharper (definitely dimmer) with only one color.
Discussion Questions (12 pts)
Summarize your diagram from part 1 – when do you have a virtual image? When does this
occur in the real world? (3pts) Virtual images occur when inside the focal distance. In the real
world, this happens with a magnifying lens or many other example.
How accurately are you able to determine f in part 2? (3 pts) Comparison to actual focal
length (2 pts) and general procedure of using a distant light source so that d(object) is basically
infinity so that the focal length is the image distance (1pts)
Based on observations made in part 2, what can you conclude about the dependence of the
index of refraction on the frequency of light? Does n increase or decrease with increasing
frequency? (2 pts) The index of refraction definitely depends on the freq of light. As freq
increases, n decreases.
What kinds of lenses are used in eyeglasses? Why? (0 pts) The answer here depends on the
glasses and the particular issue that a person has. Myopia is corrected with concave lenses
which compensate by moving the distant object that cannot be seen clearly backward onto the
retina. Hyperopia is corrected with a convex lens that moves the image of a distant object
forward onto the retina (instead of being behind)
What happened when you covered the top half of the object with a piece of paper. Did the
result agree with your prediction? Explain what is happening.
(2 pts) When the top half of the object is covered, the bottom half of the image disappears
because the image is inverted. Most students will not be surprised by this.
What happened when you covered the top half of the lens with a piece of paper. Did the result
agree with your prediction? Explain what is happening.
(2 pts) When the top half of the lens is covered, the entire image is still visible, but it becomes
dimmer. Many students will be surprised by this. The reason is that the properties of the lens
are not changing (it still has the same focal length), but only half the light passes through, so
that is why the image gets dimmer.
Lab Write up
Thin Lenses and Lens Aberrations
Pre-lab questions and exercises
1. Explain why a ray that passes through the center of a lens has the same exit angle as the
angle of incidence.
2. Describe a simple method for determining the approximate focal length of a converging
lens by using a distant light source. Use the thin lens equation to justify this method.
3. Predict which color light will have the shorter image distance, red or blue.
4. Summarize the cause of spherical aberrations and what can be done to improve images.
5. Summarize the cause of chromatic aberrations and what can be done to improve images.
Introduction
When light from an object passes through a lens, an image of the object is formed. The
radius of curvature of the two lens surfaces, the index of refraction of the lens material, and the
position of the object determine the position of the image formed by a lens. These physical
properties may be summarized by a single parameter, the lens' most important optical property:
the focal length. The focal length depends on the index of refraction of the lens material and the
radii of curvature of the two optical surfaces.
A thin lens is a lens whose thickness is small compared to its radii of curvature. This
allows us to make approximations that simplify the analysis, so that the focal length may be
obtained from the lens maker’s formula:
 1
1
1
 (n  1) 
f
 R1 R2



(1)
where f is the focal length, n is the index of refraction of the lens material, R1 and R2 are the radii
of curvature.
The position of an image is determined by the focal length and the position of the object
with respect to the lens. The equation that relates these quantities to a good approximation is:
1
1
1


f do di
(2)
where f is the focal length, do is the object distance, and di is the image distance. This equation is
known as the thin lens equation or just the lens equation.
If the properties of a lens are measured, its focal length may be determined analytically
using the lens maker's formula. The focal length may also be determined experimentally by
measuring the image and object positions and using equation (2).
The experimental determination of the focal length is made slightly more complicated by
the fact that equations (1) and (2) are not exact. Certain approximations are made in their
derivations. One of these approximations has already been mentioned—the so-called thin lens
approximation. Another approximation is that the angle between the lens and the incoming light
rays is assumed to be small. Near the outside edge of a spherical lens, this approximation fails.
The focusing properties in this region differ substantially from those predicted by the thin lens
approximation. As a result, light which passes through the outer portion of the lens is not focused
at the same position as that which passes through the center section of the lens. The result is a
blurring of the image position; no matter where you view the image, it looks fuzzy. This effect is
known as spherical aberration. Putting a mask over the outer part of the lens can reduce
spherical aberration, so that the light passes through the middle of the lens. Another approach,
which is used in the design of optical devices, is to modify the shape of the lens or to combine
several lenses.
There is one other approximation that has not been mentioned—the index of refraction of
the lens material is assumed not to depend on the frequency (“color”) of the light, when in fact, it
does. There is a different index of refraction—and therefore a different focal length—for each
frequency. This dispersion of light is what makes a rainbow. Since the light present in the
laboratory (“white light”) consists of a continuum of frequencies, the image position will be
blurred. If an object is placed a certain distance from the lens, the “red” image will be formed at
a different position from the “blue” image. As a result, in white light the image always appears a
bit fuzzy. This effect is called chromatic aberration, and can be eliminated by using a narrow
spectrum of light.
In understanding the physics of lenses, it often helps to draw ray diagrams, which show
where the image will be formed, whether it will be upright or inverted, and the magnification.
Light is reflected from the object in all directions, but when drawing a ray diagram, only a few
principal rays are used:
1. A ray parallel to the axis of the lens will pass through the focal point F.
2. A ray that passes through the focal point will emerge from the lens parallel to the axis.
3. A ray that passes through the center of the lens will continue undeflected.
In Figure 1, the object is at a distance greater than the focal length. The ray diagram shows
that the image is formed where the three principal rays converge on the far side of the lens.
Since the image is formed where real light rays converge, the image is said to be a real image,
which can be projected and viewed on a screen.
Figure 1
Note: In this figure, the image and object distances are designated by p and q.
In Figure 2, the object is at a distance less than the focal length. The light rays coming from
the object diverge after passing through the lens. They appear to be coming from a point behind
the object. This is where the image is formed. Since the real light rays do not actually pass
through the image position, this image is said to be a virtual image., which can be viewed by an
eye positioned on the opposite (right) side of the lens. These images are slightly more
complicated to visualize so you will get some experience with ray tracing in Part 1 of this lab.
Figure 2
Note: In this figure, the image and object distances are designated by p and q.
The magnification M of the image relative to the object is given by:
M 
di
do
(3)
where a positive M indicates an upright image and a negative M indicates an inverted image.
Procedure
Part 1. Virtual Image Size and Position with a Planar Bi-Convex Lens
1. Tape an approximately 2-ft long piece of paper on the table and draw a line down the
center, lengthwise. Place the bi-convex lens on the center line as in Figure 2, and trace its
outline.
2. Make five parallel light rays by setting the light box dial and aim the rays at the lens.
Mark the focal point F on the line where the rays converge. Remove the lens and measure
the focal length from the center of the lens outline. Mark on the paper the point 2f at
twice the focal length. Also mark f and 2f on the other side of the lens.
3. Draw an object arrow about 1 cm high, perpendicular to the axis of symmetry, between F
and the lens on the side nearer the light box. You are about to locate the image position of
the arrow by ray tracing using the light box and three principle rays.
4. Use the single-slit mask in the light box. Aim the ray through the point of the arrow (your
object), parallel to the center line. Trace its path both before and after it is refracted
through the lens.
5. Direct the second ray through the nearest F and through the point of the arrow. Trace its
path through the lens and beyond 2f on the far side.
6. Aim a third ray through the arrow and through the lens’ center and trace its path.
7. The rays will not converge – why not? After drawing the rays, trace each of them
backwards using dashed lines to represent virtual rays; they should converge behind the
object. Draw an arrow to that point.
8. Measure the image and object distances from the center of the lens. What is the
magnification of the lens?
9. Measure the height of the image arrow and compare it to the height of the object arrow. Is
it reduced or enlarged? Also note whether it is upright or inverted. Calculate the
magnification of the lens based on these measurements. Does it agree with your
measurement in step 8?
10. Where do you need to place the arrow to have a real image? Confirm your hypothesis by
testing with the light box.
11. Spend some time with your lab mates looking at a more complicated ray tracing tool.
There are some different options out there, but a favorite can be found embedded in a lab
from Mt. Holyoke college located here:
http://www.mtholyoke.edu/~mpeterso/classes/phys301/geomopti/micro.html (you don’t
have to do or read through that lab, just look at the simulation).
a. Can you make a microscope setup (what optics are necessary)?
b. Can you make a telescope (how is this different from a microscope)?
c. What are the effects of using an aperture on your final image?
Part 2 (DAY 2!). Exercises Using a Thin Bi-Convex Lens
1. Place the light source on one end of the optical bench with the target facing the bench.
2. Place the convex lens about 50 cm from the object (the crossed arrow target on the light
source itself).
3. Carefully measure the object distance do from the convex lens. Locate the image with the
viewing screen. The best way to determine the image distance di is to start with the
viewing screen close to the lens and move it away slowly. The image will decrease in
size and come into focus as the viewing screen approaches di. Beyond that point the
image becomes fuzzy and its size increases. The image position is the point of optimum
focus or where the image becomes sharpest. Measure di as accurately as possible and
estimate the uncertainty in this measurement.
4. Move the convex lens to at least two new positions and repeat step 3 for each new object
distance. For this part, don’t move the object any closer to the lens than about 10 cm.
5. This step should be done qualitatively - be sure to record observations carefully. The
focal length for your lens is in the range 6 to 7 cm. Start with the object about 10 cm from
the lens. One partner should slowly move the lens towards the object, while the other
partner tries to locate the image for as long as possible. You do not need to record image
distances, just observe and describe what happens. Using the lens equation, solve for di
when do is equal to f. Do your observations above seem to support what the lens equation
is telling you? Now move the lens a few centimeters closer to the object. Where is the
image? Will di be positive or negative when do is smaller than f?
6. Calculate f for each pair of measurements. Find the average of f and estimate its
uncertainty. Compare this to the actual focal length of the lens you used.
7. Set the object distance at 15 cm. Locate the image with the viewing screen and obtain as
sharp an image as possible.
8. Place the blue filter over the source, adjust the viewing screen to secure a sharp image
and record di. Which is sharper—the image with the filter, or the one without the filter?
Now replace the blue filter with a red one. If the image is no longer sharp, move the
viewing screen until it is sharp once more. You will probably need to move the screen by
only one or two millimeters. Again, record the image position. Which direction do you
need to move the viewing screen to bring the red image into focus? Why?
9. Keeping the red filter over the source and the viewing screen adjusted to the sharpest
image, insert the aperture plates directly in front of the lens on the side of the object and
note the change in sharpness of the image as the aperture is opened and closed.
10. Predict what will happen to the image when you cover the top half of the object with a
piece of paper. Test your prediction and explain your findings.
11. Predict what will happen to the image when you cover the top half of the lens with a
piece of paper. Test your prediction and explain your findings.
Conclusion/Discussion (these can be answered directly on the
worksheet)
1. How accurately are you able to determine f in part 2? How can you determine f quickly
for any lens if you don’t have a light table setup?
2. Based on observations made in part 2, with the filters, what can you conclude about the
dependence of the index of refraction on the frequency of the light? Does n increase or
decrease with increasing frequency?
3. What are some of the practical applications for what you learned in this lab? What kinds
of lenses are used in eyeglasses? Why?
4. How would you improve this lab?
Names:__________________________________________________ Group:_______________
Optics Lab: Thin Lenses (over 2 days)
Part 1: Ray Tracing
What is the height of your image?
Is it reduced or larger than the original object?
Upright or inverted?
Final magnification?
Is this what you expected? Any general comments about the ray tracing?
Can you use the simulation linked in the lab writeup to build a microscope or a telescope?
What designs/arrangements work best to magnify?
Part 2: Optic Bench Work
Convex lens: (labeled focal length: f =_____________)
do
u do
di
u di
f
uf
Find the average f and its uncertainty. Compare this to the actual focal length of your lens.
Qualitatively describe what happens when do approaches f.
Effects of filters (step 8): Initial do =_______±________ and di =_______±________
How does the BLUE filter affect the image? Is the image sharper with or without the filter?
Does the image distance increase or decrease?
How does the RED filter affect the image? Is the image sharper with or without the filter? Does
the image distance increase or decrease?
Discussion Questions
Summarize your diagram from part 1 – when do you have a virtual image? When does this
occur in the real world examples?
How precisely are you able to determine f in part 2?
Based on observations made in part 2, what can you conclude about the dependence of the
frequency of light on the index of refraction? Does n increase or decrease with increasing
frequency?
What happened when you covered the top half of the object with a piece of paper. Did the
result agree with your prediction? Explain what is happening.
What happened when you covered the top half of the lens with a piece of paper. Did the result
agree with your prediction? Explain what is happening.