Name: ___________________________
Group Members: ___________________________
___________________________
___________________________
Thin Converging Lenses
Purpose and Objectives
The goal of this laboratory experiment is to determine the properties of the image formed by the light
that refracts as it passes through a converging lens. Lenses are made of glass or of similar transparent
material, which refracts light at the surfaces. They are shaped so that they diverge or converge a
bundle of parallel rays, specifically such that parallel rays incoming to the lens cross at a point (the
focal point) after they leave. The focal length ( f ) is the distance between the lens and the focal point.
The focal length is a fixed characteristic of a given lens, depending only on the lens material and
shape. A lens that converges light is called convex, and the value of f is positive. If a lens diverges
light, it is called concave, and the value of f is negative. We deal only with converging lenses in this
lab.
In today’s laboratory experiment you will find the focal lengths of two converging lenses by three
different methods. Many of the methods involve using the thin lens equation:
(1/f) = (1/p) + (1/q)
where p is the object distance (object to lens), q is the image distance (image to lens), and f is the
focal length. For real objects and images the distances are positive. For virtual objects and images the
distances are negative. Focal lengths are positive for converging lenses (thicker in the middle than at
the edges) and negative for diverging lenses (thinner in the middle than at the edges). Your learning
objectives for this lab are as follows:



To explore refraction using a single lens and a lens and mirror combination.
To investigate methods for finding the focal lengths of thin lenses.
To verify the thin lens equation
Materials
Object lamp
Small Plane Mirror
Index Card
Modeling Clay
Masking Tape
Converging lenses (f = 10 cm and 20 cm)
Diverging Lens (f = 20 cm)
Pin or Pen
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Procedure
Part I – Converging Lens with Distant Object
When the object is very far away, p = ∞, and the thin lens equation gives q = f. Thus the focal
length is found by measuring the image distance for a distant object.
1. Place a lens in a mound of modeling clay so that the lens is perpendicular to the table and
very little of the lens is blocked by the clay.
2. Move the clay with the lens to the center of the table and turn it so that the light from some
distant source (at least 5 meters away) lines up with the lens. Affix a length of masking tape
perpendicular to the lens to act as the principal axis and place the screen (index card) on the
other side of the lens.
3. Move the screen along the principal axis until the image of the distant object is sharply
focused on it (the screen may need to be raised or lowered).
4. Using a meter stick, find the image distance. Record this distance as f.
5. Repeat steps 1 through 4 with the other converging lens.
Part II – Converging Lens with Object on the Optical Bench
In this method a real object at a finite distance is used and the focal length is calculated from the
measured image distance and thin lens equation. You will use the masking tape, lens, and screen
as an optical bench.
1. Place 100 cm of masking tape on the table to act as the optical bench. Place the screen at one
end and at the other put the object lamp.
2. In between these two place the modeling clay with one of the converging lenses.
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3. Adjust the lamp so that the filament is perpendicular to the axis of the optical bench. Adjust
the height of all elements so that the filament is just at the same height as the center of the lens
and the screen.
4. Turn on the lamp and move the lens along the bench until a clear image of the lamp is formed
on the screen. Mark the position of each item on the masking tape.
5. Using a meter stick and the marks on the masking tape find the object and image distance and
record as p and q.
6. Move the lens to find the other object and image distances that produce a clear image. Because
the image will be very large, use a large sheet of paper at the position of the screen to help
locate the image.
7. Repeat steps 4 through 6 for the other converging lens.
Part III – Converging Lens by Auto Collimation and Parallax
This method uses a process called auto collimation. If a small object is precisely at the focal point
of a converging lens, all light rays from the object which pass through the lens will form a parallel
beam along the axis on the other side of the lens. A plane mirror placed perpendicular to the
collimated beam will reflect the rays so that they return to the lens in a parallel beam and focus
back down to the focal point. In other words a real image will be formed at the position of the
object. For an object you will use a pencil point or the tip of a ball point pen.
You will determine the position of the image by using the effect called parallax. Parallax is the
apparent motion of two objects with respect to each other, due to a real motion of the observer:
objects closer to the observer appear to move past objects more distant. In this part of the
experiment, when you view the object and image together, you can tell they are at the same
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position if they exhibit no parallax as you move your head from side to side. Figure 1 illustrates
the final situation you will try to attain.
1. Position yourself and the optical bench so that you can sit and comfortably look along the
principal axis.
2. About 40 cm from your end of the bench place two lumps of clay as close together as
possible. The nearer one should have the converging lens with the longest focal length and
the other should have a plane mirror facing the lens. Mark both of their positions on the
masking tape.
3. Place a third lump of clay on the bench between the lens and your end of the bench. In this
modeling clay insert a sharp pencil or ball point pen and adjust all elements in height so that
the point of the object is just at the level of the middle of the lens and mirror.
4. Move the object along the bench while looking along the bench, through the lens, and into
the mirror, until you can see an inverted image of the object. Adjust the angle of the mirror in
order to make the image appear just above the object.
5. Move your head from side to side and observe any parallax (relative motion) between the
object and the image.
6. If the object appears to move more than the image, it is closer to you; move the object
toward the lens slightly and repeat step 5.
7. If the object appears to move less than the image, it is farther from you; move the object
slightly away from the lens and repeat step 5.
8. When the object and image appear to move together (no parallax), they are at the same
position. Mark the position of the object on the masking tape. Using a meter stick and the
marks on the masking tape, determine their separation. Record this separation as f.
9. Repeat steps 2 through 8 for the second lens.
Data
Part I
1st Lens
f (cm)
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2nd Lens
Part II
p (cm)
q (cm)
f (cm)
favg (cm)
Percent
Difference
Parts I & II
1st Lens
2nd Lens
Part III
1st Lens
2nd Lens
f (cm)
Percent Difference
Parts I & III
Analysis
1.
In the results table enter your two converging lens focal lengths from Part I.
2.
From the data of steps 5 and 6 in Part II and the thin lens equation, calculate two values of f for
each of your converging lenses. Average the two values for each lens and enter them into your
results section.
3.
Calculate the percent difference between Parts I and II. Enter these percents into your results
table.
4.
Enter your value for the focal length determined in Part III into the results table.
5.
Calculate the percent difference between Parts I and III. Enter this percent into your results
table.
6.
Using your values for p and q found in Part II, calculate the magnification of each lens.
7.
Using your values for p and q found in Part II, graph (1/q) vs. (1/p). Calculate the slope from
the graph and identify what it represents.
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