Thin Lenses
A lens is a device that produces a change in the curvature of a wavefront that passes
through it. That is, the “rays” that we use to represent the wavefronts are either converged
or diverged, depending upon Snell’s law of refraction, which in turn depends upon the shape
of the lens. In this lab, we will not concern ourselves with the application of Snell’s law to a
complex curved piece of glass, but will rather treat this lens as a simple object that can bend
light rays.
A lens is used either alone or with other lenses to produce an image of some actual
object. As implied, the object is a real entity, but the image is merely a collection of bent light
rays that, to the eye, appear to be a replica of the object. This image may be larger or
smaller than the object (that is, it may seem to be either closer than or farther than the actual
object’s distance to the observer). When an image can be projected upon a screen, we
refer to this image as a real image. If the image can only be seen by looking through a lens
we refer to the image as a virtual image.
In the simplest and most generally useful approximation, a lens can be treated in
what is known as the thin lens approximation, which obeys this simple law:
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 
p q f
In this equation, s is called the object distance. By convention, real objects are assumed to
be “in front” of the lens, and p >0. (A virtual object can be behind the lens, but this only
occurs for multiple-lens configurations, which will not be dealt with here.) Depending upon
the location of the object and one property of the lens, the image distance, q, may be either
positive (real image, in back of the lens) or negative (virtual image, in front of the lens). The
important property of the lens is its focal length, f, which is the distance from the lens at
which the lens converges incoming parallel rays into a single point. For a converging lens,
this is a positive number, measured either in meters or centimeters. For a diverging lens,
this number is negative. It is the focal length that determines the location of the image given
an object distance.
Part 1: Focal length of a converging lens
Before work can begin, you must verify the focal length of your converging lens. (It should
be labeled +100mm, +150mm or +200mm.) Use a distant object (more than a couple
meters away) on one side of the lens and find what image distance gives a well-focused real
image on a screen located on the opposite side of the lens. This image distance is
approximately equal to the focal length, f, of the lens.
Part 2: Properties of lenses
A. For the first part of this lab, you will use a lighted shape as a real object. You must place
the object on one end of the optical bench and then place the converging lens between
the object and a screen on the opposite end of the bench. The object-screen distance
should be between 90 and 60 cm. Move the various elements about until you have a real
image projected onto the screen. This real image may be of the whole object or merely
part of it. Record the object and image distances and verify, in your lab report, that they
satisfy the thin lens equation.
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B. Calculate the magnification, h’/h, for this image. h’ is the height (or width) of the image
and h is the height (or width) of the object. Compare this measured magnification with
the theoretical value, M = q/p. Note that, by convention, a negative M indicates an
inverted image (h’ is negative) and a positive M is right-side-up.
C. Experiment with the position of the lens. See if you can find another location of the lens
that provides a focused image on the screen. As in step A above, record the object and
image distances and verify that this arrangement also satisfies the thin lens equation.
Repeat step B for this new arrangement also.
D. Next, move the object closer to the lens until the object distance is smaller than the focal
length of the lens. What type of image is predicted by the lens equation? How would you
observe such an image? Describe what you observe. Does it qualitatively agree with the
predictions of the thin lens equation for magnification? (Note: these questions need to be
answered in your lab report).
E. Using eyeglasses from some member of your group (or borrow someone else’s or even
the instructor’s), examine them briefly and see if you can conclude, based on its
appearance compared to your converging and diverging lenses, whether the eyeglasses
are diverging, converging, or neither. Important: you are only comparing these
glasses with the converging and diverging lenses you are provided with. Do not
try to insert the glasses into the experimental apparatus.
Discussion Questions
1. In part 1, is your measured focal length consistent with the thin lens equation? You
should include your mathematical determination in your lab report.
2. Answer the question in part 2 one at a time, labeling each answer with the appropriate
letter.
3. In William Golding’s novel Lord of the Flies the boys use Piggy's eyeglasses to focus
sunlight into an intense, hot spot to start a fire. In optometry, converging lenses are used
to correct farsightedness and diverging lenses are used to correct nearsightedness. Is
Piggy nearsighted or farsighted?
D. Boucher 4/2012
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