Converging Lens

```Converging Lens
Xiaoya Wu
Marguerite Daw
Purpose
 Examine
 object
the relationship between:
distance vs. image distance
 object height vs. image height
 image height vs. object distance
Hypothesis
 As
object distance increases, image
distance decreases
 As object height increases, image height
increases
 As object distance increase, image height
decrease
Materials
Lamp
 Marked track
 Lens
 Screen
 Object
 Flashlights
 Dark Room

Ring stand
 Clamps
 Cardboard (for when
small screen is too
small for part 2)

Setup
Procedure (Part One)
1.
2.
3.
4.
5.
6.
7.
8.
Measure the focal length by holding the lens and screen (mounted on the
track) up to a distant image. Find the distance where the image is the
most focused.
Set up the stationary lamp at the zero mark of the track. Use ring stand
and clamps to fix the lamp. Make sure to measure the height of the
object on the lamp.
Lay out the tracks and affix the lens at a distance of 15 focal distance
away from the lamp/zero mark.
Move the screen until a focused image is formed. Measure the image
distance and height.
Decrease the object distance by moving the lens closer to the lamp by 1
focal distance. Repeat 4.
When object is 3 focal length away, decrease the object distance by 5.0
cm.
When object is close to 2 focal length away, decrease the object distance
by 2.0 cm.
Stop when image gets too big to measure on the screen
Data Table
Constants:
Image Height (L)= 1.9 cm
Focal Length = 19.7 cm
Method 1
-Both Asymptotes
Method II
-One Asymptote
Since the last three
points were very difficult
to focus, we decided to
leave them off.
Mathematical Analysis
Slope Significance/Model
Error Calculations
Constants: focal length = 19.7 cm
Y-intercept
Mathematical Analysis
What does this mean?


Looking at the intercept, we noticed that the x- and yintercepts are very close to being the same. Also the
slope of the graph is -1. This suggests that the sum of
1/Image Distance and 1/Object Distance is a constant,
which is 1/Focal Length.
Thus,
Error Calculations
Constants: focal length = 19.7 cm
Slope



Experimental Value = -1.05
Actual Value = -1.00
Absolute Error
=|-1.00 - -1.05|
= .05

Relative Error
=.05/-1.00
= .05
=5%


Y-intercept
Experimental Value =.0509 (1/cm)
Actual Value = 1/19.7 cm
= .0508 (1/cm)

Absolute Error
=|.0508 (1/cm) - .0509 (1/cm) |
=.0001 (1/cm)

Relative Error
=.0001 (1/cm) / .0508 (1/cm)
= .002
= .2%

The last few points were
left out because their
image heights were not
accurate due to
difficulties in focusing.
Mathematical Analysis
Error Analysis
Constants:
Image Height = 1.90 cm
Focal Length = 19.7 cm
Procedure (Part Two)
1.
2.
3.
4.
5.
Set up the lens at 1.5 focal length from the lamp.
Measure the height of the object. Place the object in
from of the lamp.
Adjust the cardboard screen until the image is focused.
Measure the image height.
Repeat with objects with different heights.
Repeat 1-4 at 2.5 focal length.
Data Table
Mathematical Analysis
1.5 Focal Length
2.5 Focal Length
What Just Happened?
Do = 1.5f
Do = 2.5f
Error Analysis
1.5 Focal Length



Experimental Value = 2.02
Actual Value = 2.00
Absolute Error
2.5 Focal Length



=|2.00 – 2.02|
= .02

Relative Error
= .02/2.00
= .01
= 1%
Experimental Value = .604
Actual Value = .500
Absolute Error
= |.500 = .604|
= .104

Relative Error
= .104 / .500
= .208
= 20.8%
Source of Error


The main source of error was measuring the image height.
It was especially difficult when the image was small. For
the first few points, there was no discernible difference in
the height. The ruler was also not always held steady
when measuring.
Another source was getting the image completely focused
and then measuring the image distance. At some points
the distance could have been a range of values of + or –
1cm.
Ray Diagram
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Ray Diagram
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Ray Diagram
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Ray Diagram
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Ray Diagram
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Thank you
The End
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