Converging Lenses
Graphical Analysis
By Chris Cho and Dan Fan
Purpose
 Determine the
relationship between
object distance and
image distance for
real images produced
by a converging thin
lens.
 Determine the
relationship between
object height and
image height.
Hypothesis
 Object distance is inversely proportional to image distance.
 Object height is directly proportional to image height.
Materials
 Cart Track
 White Screen
 Converging Lens
 Light Source
 Cut-out Arrows of Various Sizes on
Cardboard
 Cut-out Number “4” on Cardboard
 Meter Stick
 Chris’ Mom
To Find the Focus
Obtaining the Focus length.
1. Place the screen at a given length on
the cart track so that there is enough
room to place the converging lens on
the side that points toward the window.
2. Point the apparatus toward the
window and locate a specific object in
the far distance.
3. Observe the image on the screen and
focus the image by adjusting the
distance between the screen and the
lens.
4. When the image is “perfectly”
focused, measure the distance from the
screen to the lens and this will be the
focus length.
Focus Diagram
General Lab Procedure
1. Start by placing the converging
lens a total of 15 focal lengths away
from the object (the distance
between the lens and the object is
the object distance). Adjust the
screen so that the image becomes
clear. (the distance between the
screen and lens is the image
distance. Shorten the object distance
by 1 focal length increments and
adjust the screen while measuring
the image distance and object
distance each time. Shorten the
object distance by smaller
increments once you approach a
distance of 2 focal lengths.
2. Move the converging lens 1.5 focal lengths
away from the object. Place a cut-out arrow in
front of the light source and adjust the image
distance until the projected image is clear.
Measure both the real and the projected arrow’s
length. Do the same with arrows of varying
sizes. Repeat the same procedure with a 2.5
focal length object distance.
Distance Exploration Table
Image Distance vs Object Distance
Image Distance vs 1/ Object Distance
1/ Image Distance vs 1/ Object Distance
1/ Image Distance vs 1/ Object Distance
Mathematical Analysis
Slope Error
Accepted Value = -1
Absolute Error = |Experimental Value – Accepted Value|
Absolute Error = |-1 - -1.032|
Absolute Error = 0.032
Relative Error = Absolute Error / Accepted Value
Relative Error = 0.032 / 1
Relative Error = 0.032 or 3.2%
Y-Intercept Error
Accepted Value = 1/f (which also 1/m units) = 1/19.57 = 0.0511
Absolute Error = |Experimental Value – Accepted Value|
Absolute Error = |0.0511 – 0.0510|
Absolute Error = |0.0001|
Relative Error = Absolute Error / Accepted Value
Relative Error = 0.0001 / 0.0511
Relative Error = 0.002 or 0.2%
Image Height vs Object Height Table
Image Height vs Object Height
Graph
Image Height vs Object Height Analysis
Drawing Ray Diagrams
 Drawing Ray Diagrams:
 Draw a ray from a point on the object parallel to the principle axis
to the center of the lens. Draw another line extending from that
point through the foci on the opposite side of the image. (can be
done because of the definition of focus)
 Draw a second ray from that point through the point in which the
principle axis intercepts the lens.
 Draw a third ray through the focus to the lens. Draw another line
extending from that point parallel to the principle axis.
 The point of intersection is the corresponding image point to the
original object point.
Ray Diagram (around 1.5 foci)
Object
2f
Image
f
f
2f
Ray Diagram (around 2 foci)
Object
2f
f
f
Image
2f
Ray Diagram (around 2.5 foci)
Object
2f
Image
f
f
2f
Fin