Lab
Determining the Focal Length of a Converging Lens
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Introduction
In this lab, the student will determine the focal length of a given lens by using an optical bench to make measurements of object and image distances. Students will be asked to make additional observations to further their knowledge of lens properties.
Part I: Determining the Experimental Focal Length of your Lens
1. Measure the diameter of the quarter (h
_{o}
) and record your measurement, in centimeters, below.
2. Position your quarter (object) and the lens so that the diameter of the quarter's image on the screen is less then 1.5 cm. Make sure that the image is brought into sharp focus.
3. Measure the distance between the object and the lens (s
_{o}
). Record the measurement, in centimeters, in the table below.
4. Measure the distance between the lens and the screen (s
_{i}
). Record the measurement, in centimeters, in the table below.
5. Use the thin lens formula
or equivalently,
, along with your measured values for s
_{o}
and s
_{i}
to calculate the focal length of your lens. Show your work on this paper and record your values in the table below.
6. Repeat steps 2-5 for image heights equal to the diameter of your quarter and then for greater then 5.0 cm.
Our quarter's diameter (h
_{o}
) equaled ____ cm
Trial
image height
criteria
measured
image height
measured
object distance
measured
image distance
calculated
focal length
#1
h
_{i}
< 1.5 cm
#2
h
_{i}
= h
_{o}
#3
h
_{i}
> 5.0 cm
What was your average focal length (f
_{avg}
) in cm?
Part II: Scaled Lens Diagrams
Using your measured object height (h
_{o}
), measured image heigth (h
_{i}
), measured object distance (s
_{o}
), and your measured image distance (s
_{i}
), draw a ray diagram for each trial. Although you may scale your values for s
_{o}
and s
_{i}
,
draw your object and image the EXACT heights that you measured
in Part I.
Using two rays, confirm the location of the lens and measure your diagram's scaled focal length. Before reporting your focal length values in the chart below, remember to reproportion them to the original size of the optical bench's measurements. Each member of the group must complete at least one ray diagram. Place that member's name on the top of their diagram's paper.
Trial
focal length
h
_{i}
< 1.5 cm
h
_{i}
= h
_{o}
h
_{i}
> 5.0 cm
Based on your ray diagrams which trial's data for the lens' focal length agreed the best with your previously calculated value?
h
_{i}
< 1.5 cm
h
_{i}
= h
_{0}
h
_{i}
> 5.0 cm
Based on all of your data (calculations and ray diagrams), what is the group's consensus on best value for the lens' focal length? State your value and explain why you made your decision.
Part III: Affect of Covering the Lens
Using the last setup on your optical bench (h
_{i}
> 5.0 cm) take a card and slowly cover the lens while watching the affect of the image.
Describe what happens to the image (what part of the image disappears; what happens to the brightness of the image; at what point are you unable to see the image?)
Part IV: Magnification of the Image
Notice in the following diagram that the two green triangles are similar right triangles.
We can therefore state that:
Rearranging these ratios gives us the expressions:
Hence there are two alternative ways to determine the magnification of an image.
Using your measured values in the table from Part I, calculate both magnifications for each trial.
Trial
h
_{i }
/ h
_{o}
s
_{i }
/ s
_{o}
h
_{i}
< 1.5 cm
h
_{i}
= h
_{o}
h
_{i}
> 5.0 cm
Based on the magnification information in the above table, which trial had the best agreement?
h
_{i}
< 1.5 cm
h
_{i}
= h
_{0}
h
_{i}
> 5.0 cm
Was this trial also your best ray diagram?
Yes
No
What was this trial's percent difference?
Part V: Images Located an "Infinite Distance" from the Lens
To complete this section, you must take your lens (in its holder) and your screen (with its holder) to the window station. With the blinds partially open, use your lens to form an image of an object located outside the room. Once you have a clear image, measure the distance from the lens to the screen.
What was your image distance in cm?
What property of the lens does this distance most closely represent?
Part VI: Images within the Focal Length
Take your lens and place it on the candle printed on your paper below:
Slowly lift the lens above to candle printed on your paper while looking through the lens, until you reach the focal length.
What happens to the image as you look through the lens when you lift the lens off the paper?
Could the image that you see through the lens be projected onto a screen? Why or why not?
Describe what you see when you have lifted the lens the focal length above the paper?
Part VII: Determining the Lens Position
1. Ask your lab instructor for the distance between your object ( d
_{o}
) and your screen ( d
_{i}
) and record the value below. You will be asked to turn in your lens to the instructor.
s
_{o}
+ s
_{i}
= ___ cm
2a. What was your agreed upon focal length in Part II?
2b. Using your focal length and the required object-image separation distance (conclusion 1), determine the required distance that the lens should be placed from the object (s
_{o}
). This may be done with ray diagrams
(see hint)
or mathematically.
s
_{o}
= ___ cm
2c. Which type of magnification are you expecting for this image?
reduced
the same size as the object
enlarged
2d. Calculate the numerical value for your predicted magnification based on your values of s
_{o}
and s
_{i}
from conclusion 2b.
Don't forget that you know the value of s
_{o}
+ s
_{i}
.
3a. Request your lens back from your lab instructor. In the presence of your instructor, place the lens on to the optical bench and observe the clarity of your image. Then re-position the lens so that the image is brought in to as sharp a focus as possible. Measure the final "best" distance between the object and the lens (s
_{o}
). Record your measured value here in cm.
3b. Calculate the numerical value for your actual magnification based on your values for s
_{o}
and s
_{i}
in conclusion 3a.
Don't forget that you know the value of s
_{o}
+ s
_{i}
.
3c. Determine the percent error between your experimental predicted value for your magnification (conclusion #2c) and the magnification calculated from your lab instructor's measured value of s
_{o}
in conclusion #3b.
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Worksheet:
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APP -
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Lenses
CP -
Plane Mirror Reflections
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Refraction of Light
CP -
Snell's Law
CP -
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NT -
Image Distances
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Laser Fishing
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Mirror Length
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Reflection
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Underwater Vision
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An Extension of Snell's Law
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Basic Principles of Refraction
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Converging Lens Vocabulary
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Diverging Lens Vocabulary
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Lensmaker Equation
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Plane Mirror Reflections
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Refraction and Critical Angles
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Refraction Phenomena
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Refraction Through a Circular Disk
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Refraction Through a Glass Plate
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Refraction Through a Triangle
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Snell's Law Calculations
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Spherical Mirror Equation #1
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Spherical Mirror Equation #2
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Spherical Mirrors: Image Patterns
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Thin Lens Equation #1: Converging Lenses
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Thin Lens Equation #2: Converging Lenses
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Thin Lens Equation #3: Both Types
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Thin Lens Equation #4: Both Types
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