physics lab 7
mbedichek2001
PHYS1110Lab07-LensesandImageFormation.pdf
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Augusta Technical College
PHYS 1110L - Online Lab 7: Lenses and Image Formation
Objectives:
The purpose of this experiment is to investigate properties of thin lenses and image formation. We
will use simulation software to study focal length, object and image distances, and the
magnification of thin lenses.
Equipment:
• Computer
• Scientific Calculator
• Ruler with cm scale
• Lenses and Mirrors Simulation Software (The Physics Classroom)
Theory:
• For thin lenses, the relationship between the focal length f, the distance between the object and
the lens do, and the distance between the image and the lens di, is similar to spherical mirrors
and is given by:
io ddf
111 +=
The object distance do is positive if the object is located in front of the lens (real), and negative
if it is located behind the lens (virtual).
The image distances di is positive if the image is located in behind of the lens (real), and negative
if it is located in front of the lens (virtual).
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• For thin lenses, the focal length f is given by the lens maker’s equation:
−−=
21
11 )1(
1
RR n
f
Where n is the index of refraction of the lens material, R1 is the radius of curvature of the first
lens surface, and R2 is the radius of curvature of the second lens surface.
The focal length f is positive for converging lenses and negative for diverging lenses.
The radii of curvature R1 and R2 are positive if they are on the outgoing side of the lens and
negative if they are on the opposite side.
• If the object is very far from the lens, then:
fdd io =→
• The magnification M of a lens is defined as the ratio of image size hi to object size ho, and it can
be determined from:
o
i
o
i
d
d
h
h M −==
If the image is upright, then M is positive, and if the image is inverted, then M is negative.
• A virtual image cannot be viewed on a screen. It forms where the backward extensions of
diverging rays cross. You can see a virtual image by looking at it through a lens or mirror.
• Principle rays are convenient to use in ray diagrams to trace the path of the rays and determine
the formation of the image. Three principle rays for concaving and diverging lenses are shown:
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Part A – Converging Lens with f = 18.8 cm:
• Open the Lenses and Mirrors Simulation Software:
https://www.physicsclassroom.com/Physics-Interactives/Refraction-and-Lenses/Optics-
Bench/Optics-Bench-Refraction-Interactive
➢ Click the icon in the top-left corner or drag the icon in the lower- right corner of the
simulation fame to maximize the simulation.
➢ In the simulator leave all rays on “Ray 1, 2, 3 ON” (bottom left).
➢ The values of the focal length (𝒇), object distance (𝒅𝒐), object height (𝒉𝒐), image distance
(𝒅𝒊), and image height (𝒉𝒊) are given on the bottom right.
➢ Note: The given values in the simulation are all “absolute values”. When recording the
values in the data tables be sure to include the correct signs, as discussed in the theory.
• On the top right, select “Converging” to change lens to a Converging lens.
• In the simulator set: Absolute value of “Focal Length” = 18.8 cm, and “height” = 19.0 cm,
shown in the above figure.
• Position the object (candle) so it is located at the object distance do = 70.0 cm to left of the lens.
• Record the object distance (𝒅𝒐), object height (𝒉𝒐), image distance (𝒅𝒊), and image height (𝒉𝒊) in the below table.
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• Repeat the above procedure for the rest of the object distances do given in the below table for a
total of 5 trials. Record the data in the below table.
• Save a screenshot (screen capture) of the simulation showing the lens, object, and image for one
of the trials to include in the graphs section of your report.
Part B – Converging Lens with f = 22.8 cm:
• In the simulator set: Absolute value of “Focal Length” = 28.8 cm, and “height” = 19.0 cm, as
shown in above figure.
• On the top right, select “Converging” to change lens to a Converging lens.
• Repeat the procedure from Part A for the object distances given in the below table for a total of
5 trials
• Record the object distance (𝒅𝒐), object height (𝒉𝒐), image distance (𝒅𝒊), and image height (𝒉𝒊) in the below table.
• Save a screenshot (screen capture) of the simulation showing the lens, object, and image for one
of the trials to include in the graphs section of your report.
Part C – Diverging Lens with f = –22.8 cm:
• In the simulator set: Absolute value of “Focal Length” = 28.8 cm, and “height” = 19.0 cm, as
shown in above figure.
• On the top right, select “Diverging” to change lens to a Diverging lens.
• Remember that for a diverging lens the focal length is negative.
• Repeat the procedure from Part A for the object distances given in the below table for a total of
5 trials
• Record the object distance (𝒅𝒐), object height (𝒉𝒐), image distance (𝒅𝒊), and image height (𝒉𝒊) in the below table.
• Save a screenshot (screen capture) of the simulation showing the lens, object, and image for one
of the trials to include in the graphs section of your report.
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Analysis:
• Part A – Converging Lens with f = 18.8 cm:
1. For each of the trials, calculate the accepted value of the image distance di using the lens
equation given in the theory section, the given value of the object distance do, and the given
value of the focal length f. Record values in the below summary of results table.
2. Remember to use the correct signs for all values when performing the calculations, as
discussed in the theory section, and be sure to calculate the image distance di, not 1/di !
3. Compare the experimental and the accepted values of the image distance di by calculating
the % errors. Record values in the below table.
Percent error is used to compare experimental (measured) to accepted (calculated) values:
% Error = %100 ||
−
A
EA ; Where: A = accepted value and E = experimental value.
4. For each of the trials, calculate the experimental value of the magnification M from the
measured ho and hi values, and the accepted value of the magnification M from the measured
do and di values. Record values in the below summary of results table.
5. Compare the experimental and the accepted values of the magnification M by calculating
the % error. Record values in the below table.
6. How do the values compare what factors do think may cause there to be a difference between
these values? Discuss in your lab repot.
7. Based on your observations, describe the image position, size, and orientation for object
distances: do > 2f, do = 2f, f < do < 2f, do = f, and do < f. Discuss in your report conclusion.
8. Remember to include in the graphs section of your report a screenshot (screen capture) of
the simulation showing the lens, object, and image for one of the trials.
• Part B – Converging Lens with f = 28.8 cm:
1. For each of the trials, calculate the accepted value of the image distance di using the lens
equation given in the theory section, the given value of the object distance do, and the given
value of the focal length f. Record values in the below summary of results table.
2. Remember to use the correct signs for all values when performing the calculations, as
discussed in the theory section, and be sure to calculate the image distance di, not 1/di !
3. Compare the experimental and the accepted values of the image distance di by calculating
the % errors. Record values in the below table.
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Percent error is used to compare experimental (measured) to accepted (calculated) values:
% Error = %100 ||
−
A
EA ; Where: A = accepted value and E = experimental value.
4. For each of the trials, calculate the experimental value of the magnification M from the
measured ho and hi values, and the accepted value of the magnification M from the measured
do and di values. Record values in the below summary of results table.
5. Compare the experimental and the accepted values of the magnification M by calculating
the % errors. Record values in the below table.
6. How do the various accepted and experimental values compare and what factors do think
may cause there to be a difference between these values? Discuss in your lab repot.
7. Based on your observations, describe the image position, size, and orientation for object
distances: do > 2f, do = 2f, f < do < 2f, do = f, and do < f. Discuss in your report conclusion.
8. Remember to include in the graphs section of your report a screenshot (screen capture) of
the simulation showing the lens, object, and image for one of the trials.
• Part C – Diverging Lens with f = –28.8 cm:
1. For each of the trials, calculate the accepted value of the image distance di using the lens
equation given in the theory section, the given value of the object distance do, and the given
value of the focal length f. Record values in the below summary of results table.
2. Remember to use the correct signs for all values when performing the calculations, as
discussed in the theory section, and be sure to calculate the image distance di, not 1/di !
3. Compare the experimental and the accepted values of the image distance di by calculating
the % errors. Record values in the below table.
Percent error is used to compare experimental (measured) to accepted (calculated) values:
% Error = %100 ||
−
A
EA ; Where: A = accepted value and E = experimental value.
4. For each of the trials, calculate the experimental value of the magnification M from the
measured ho and hi values, and the accepted value of the magnification M from the measured
do and di values. Record values in the below summary of results table.
5. Compare the experimental and the accepted values of the magnification M by calculating
the % errors. Record values in the below table.
6. How do the various accepted and experimental values compare and what factors do think
may cause there to be a difference between these values? Discuss in your lab repot.
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7. Based on your observations, describe the image position, size, and orientation for object
distances: do > 2f, do = 2f, f < do < 2f, do = f, and do < f. Discuss in your report conclusion.
8. Remember to include in the graphs section of your report a screenshot (screen capture) of
the simulation showing the lens, object, and image for one of the trials.
Lab Report:
• When writing the lab report, you must review and follow very carefully the Physics Lab Report
instructions and outline document.
• In your lab report, include the Title Page, Objectives, Theory, Equipment, Data, Graphs and
Screenshots, Calculations, Conclusions, Sources of Error, and References.
• Remember to show all equations and calculations in detail and to round the results to the correct
number significant digits and precision.
• In the conclusions section, be sure to summarize the final results, comment on the agreement
or disagreement of the results with the theory or expectations, answer analysis questions, and
discuss what you personally learned from this experiment and your observations/comments.
• Remember to also answer and discuss all analysis questions in your conclusions section.
• Submit your complete lab report electronically by the due date!
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Physics - Online Lab: Lenses and Image Formation
Tables of Data and Results
• Part A – Converging Lens with f = 18.8 cm:
Experimental (measured) values from simulation:
Trial do (cm) di (cm) ho (cm) hi (cm)
1 70.0
2 37.6
3 30.0
4 18.8
5 10.0
Summary of results:
Trial Exp. di
(cm)
Acc. di
(cm) % Error Exp. M Acc. M % Error
1
2
3
4
5
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• Part B – Converging Lens with f = 28.8 cm:
Experimental (measured) values from simulation:
Trial do (cm) di (cm) ho (cm) hi (cm)
1 70.0
2 57.6
3 46.0
4 28.8
5 15.0
Summary of results:
Trial Exp. di
(cm)
Acc. di
(cm) % Error Exp. M Acc. M % Error
1
2
3
4
5
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• Part C – Diverging Lens with f = –28.8 cm:
Experimental (measured) values from simulation:
Trial do (cm) di (cm) ho (cm) hi (cm)
1 70.0
2 57.6
3 46.0
4 28.8
5 15.0
Summary of results:
Trial Exp. di
(cm)
Acc. di
(cm) % Error Exp. M Acc. M % Error
1
2
3
4
5
