for Astronomy & Cosmologies, spring 2013
by Dr. E.J. Zita, The Evergreen State College
Adapted from Grinnell optics workshops, Phil Pearl's thin lens workshop,
and Dale Ferguson's telescope workshop.
This workshop is designed to show you how lenses
affect light. By bending light rays, lenses can focus light (onto camera
film...), form images (on your retina...), defocus light (useful in some
corrective lenses), and change the sizes of images (telescopes, microscopes...)
Lenses let us more clearly see objects that are too distant or too small
for naked eyes. Lenses in telescopes help bring the stars to Earth.
Do parts A and B below; leave C for the very end in
case you have extra time, maybe design some investigations of your own...
and turn in the survey before you leave. Have
- To experience image formation by lenses.
- To better understand the behavior of light.
- To build a telescope.
- To understand how a simple refracting telescope works
(A) Make an image:
By holding a lens at the window or in the shade, and placing a screen behind the lens at
the focal distance, you can see that a real image of an illuminated object appears on the screen.
a telescope: If you remove the screen, the real image is still
there in space, and it can be examined with a magnifying glass. That is
(C) Further investigations:
Play with different lenses. If you have time, investigate how the
relative positions (and focal lengths) of lenses affect image locations
and sizes, more carefully and quantitatively.
assorted lenses and/or magnifying glasses
blank 3x5 cards
rulers and meter sticks
a lamp to shine on a clock on the wall
illuminated arrows, lens holders, optical benches (if available)
(A) A real image forms at the focal point
of a convex lens.
Light bounces off a tree (for example) in all directions. The few light
rays that reach you from a distant tree are traveling nearly parallel to
each other. When those parallel rays come through your lens, the lens will
focus them at some point in space. If you move a blank card to that point, you
can see that the focused rays form an image (on the card) of your object
(the tree). The focal length is the point at which the lens will
focus distant light (parallel rays) into an image. The focal length
(f, or focal point) of a lens turns out to be half the radius of curvature
R of the lens (Fig.a).
|Fig.(a) Convex lens
||Fig.(b) Refracting telescope made of two convex lenses
Measure the focal lengths of several lenses: Choose convex
lenses to start with. You can feel that they curve out, not in (concave),
on both sides, even if you can't see the curvature.
Imagine putting camera film or your retina in place of the card. The light
of the image excites an electromagnetic or chemical response on the surface
it impacts. Notice that the point where objects focus appears independent
of their color or size.
Go to the window or stand outside in the shade. Choose a distant,
sunlit object such as a tree.
Hold a lens in one hand and a blank 3x5 card in the other. Vary
between them until a clear image forms on the card.
Is the image upright or inverted? What else do you notice about the
image? Light rays actually converge in space at the position of this
image, so we call it a 'real' image. The screen reflects these light rays
into your eyes (and other directions).
Have a partner measure the distance between the card and the (center of)
the lens. Write down the focal length of each lens.
Discuss what you see and record your observations.
(B) A simple refracting
telescope has an eyepiece near the focal point of the objective lens (Fig.b)
Get two convex lenses, one highly curved (small f2: the eyepiece)
and a flatter one, with a very slight curve (large f1: the objective
lens). You might use a magnifying glass for one of your
Fix the flatter objective lens on the optical bench and use your 3x5 card
to find the image of a distant object (e.g. an illuminated wall
clock inside, if the trees outside are too dim). If you don't have
an optical bench, have one partner hold the lens still at the 0 end of
a meter stick, and the other partner measure the location of its image (f1).
- Check the focal length of your smaller lens (f2).
Then place your highly curved eyepiece lens so that its focal point is at the objective's focal point. See Fig.b. What is the total distance between the (center of) the two lenses, in terms of f1 and f2?
Look straight through the eyepiece and the objective, at your distant object.
The eyepiece will direct the image light into your eyes as parallel rays. Does
it look like the object is closer or further? Larger or smaller? Move the
lens and your eye around until you can see the effect clearly. Help
your partner see it.
Discuss what you see and write down your observations.
Magnification: Try to see the clock itself in the same field of
view as your magnified image of the clock, one with each eye. Estimate
how much bigger the image appears than the object. The ratio M= (-image
size/ object size) is the magnification. (The minus sign is for the orientation of the image: is it right side up or upside down?)
How does M compare to the ratio
of your lenses' focal lengths?
Extra: look through your neighbors' telescopes. How
does their magnification compare with yours? What does this have
to do with the ratio of the focal lengths of their lenses?
C: More advanced investigations - optional
(C.0) It's also possible to make a telescope with a concave eyepiece. Try it if you have time. What size works for your objective? Do you notice any difference in the image?
(C.1) You have seen that images of distant objects form at
the focal point of a lens. Images of close objects form
not at the focal point, but at a point that depends on the distance
between the object and the lens. The lighted arrows are convenient objects
for investigating this. Mount a lighted arrow on one end of the optical
bench, and a card on the other (no lens yet). Move the card back and forth;
can you get an image of the arrow to focus clearly on the card? Now choose
a lens to mount between the card and the lighted arrow, at some arbitrary
(a) Move the lens and/or the card around until you get a clear image
of the arrow on the card. Measure the object distance, p, between
the object and the lens, and the image distance, q, between the
image and the lens, and keep track of them.
(b) Move the lens away from the light (increase p). Where do you have
to move the card to find the image? Does q increase or decrease? Does the
image get bigger or smaller?
(c) Remember to record the focal length f of your lens.
(d) Discuss your observations and write down a sentence that
summarizes - in words - how the object distance depends on the image
(C.2) Thin lens equation: (1/f) = (1/p) + (1/q)
Check this relation by calculating (1/p) + (1/q) for (a) and (b) above.
How do your results compare to the focal length f of your lens? The
results may not match perfectly. Why not?
(C.3) Magnification M=(-q/p) = relative size of image, compared
to object, as you may have discovered above. Since the image and the object
subtend the same angle from the lens, the larger is further away. An object
close (small p) to the lens (but not inside the focal length...) yields
a large image (large q) far from the lens (consider a magnifying glass).
An object far from the lens (large p) yields a small image close to the
lens (small q). Calculate the magnification M for your setup above. How
does it compare to your observations about the relative size of the image
and object, and their respective distances from the lens?
(C.4) Signs: Your p and q (and f) are positive numbers (for real
objects and images, and converging lenses), so your M is negative. Does
negative M correspond to an upright or inverted image?
(C.5) Predictions and tests: Pick a different lens whose f you
know. Mount it a fixed distance p (greater than f) from your lighted arrow.
Use the simple equation above to predict where the image will be (calculate
q). Check your prediction by moving the card around until you find the
image, to measure q. How do your results compare? How does the magnification
change? What could contribute to a slight mismatch between your calculations
and your observations?
Please fill out the survey
about the workshop: What surprised you? What did you learn?
What new questions or ideas do you have?
Maintained by: E.J. Zita