Perhaps the simplest optical instrument is the lens
magnifier. Without optical aid, we cannot “see” things
close up. The eye will simply not focus closer than about
0.25 m (unless you are nearsighted!). But an object places
just inside the focal point of a converging lens will
produce a large virtual image that can be viewed more
easily. Let’s look at our Convex Lens again.
Her we can see that the ratio of the
heights of the subject and image, the magnification M
Usually we are able to get good magnification and place
the image near 0.25 m if the object is close to the focal
point on the object side of the lens. Using i ~
0.25 m and s ~ f, we get
as long as f is measured in meters. (For f
in cm, the constant in the numerator is 0.25 x 100 = 25).
The standard optical microscope consists of two
(each can be a compound lens). By placing the object to be
observed very close to the focal point of the first or
objective lens, a larger real (but inverted) image will be
produced. This real image is then observed with a second
lens, the eyepiece, which acts as a magnifier to make the
image even larger. If you wear eyeglasses or
glasses, removing them will allow you to view the
The net magnification of the entire
system is the product of the magnifications of the
objective and eyepiece. For these we just use the
magnifications given for a simple lens and a magnifier:
Because the image is much larger than the object, it
usually requires that the object be brightly lit, or it
will be too dark to see well.
Another practical limit on an optical microscope comes
from the fact that the wavelength of visible light is so
“large”. The fineness of detail that can be observed,
measured in radians, is given by Rayleigh’s criterion:
where d is the diameter of the opening through
which the light passes (such as the objective), and l is
the wavelength of light used. This limitation comes from
the wave properties of light. Light passing through a
narrow opening undergoes diffraction, which spreads the
beam out. Diffraction is basically just the interference
pattern of a light wave with other portions within the
same opening instead of a different opening.
Better resolution can be obtained using UV light, but
that only helps a little.
Electrons have much smaller wavelengths than visible
light, and so can be used to see smaller details. This is
the basis of the electron microscope, which uses magnetic
fields to focus the electrons. However, this is getting
off the subject of light & color….
Telescopes come in many different designs. Those that
use a lens as the objective to gather and focus the light
are refracting telescopes, while those that do this with
mirrors are reflecting telescopes.
The first telescopes were refractors that used a convex
lens to form an inverted image of a distant object, and
used a concave lens to invert this image to an upright
orientation as well as provide some additional
magnification. Because this was the sort of device Galileo
used to make the first important telescopic discoveries in
astronomy, it is usually referred to as a Galilean
However, Kepler found that greater magnification could
be obtained using an eyepiece that was a convex lens, at
the expense of keeping the inverted orientation of the
image formed by the objective.
Refracting telescopes used in astronomy are of the
Keplerian type, while the upright image of the Galilean
design is usually preferred for terrestrial observing.
The critical optical parameters for an astronomical
telescope are its light-gathering power, angular
resolution, magnification, and image brightness.
The greater the diameter of the objective, the greater
the surface that will intercept the light from an object.
If one is dealing with faint sources, this is usually the
single most important criterion. For this reason,
astronomers “label” telescope sizes by the diameter of
their objectives (lens or mirror) and try to make it as
large as possible. If the diameter of the telescope is D
meters, then the surface area intercepting the light is
The largest optical telescopes today have diameters of
8-10 m. By contrast, the inner diameter of the iris in the
human eye, after dark adaptation, is about 1/2 cm.
Although the diameter D is generally much larger
than the wavelength of light, it is not infinitely bigger,
and Rayleigh’s criterion still applies. Larger diameter
objectives and smaller light wavelengths improve the
situation. (As a practical matter, atmospheric turbulence
will dominate over diffraction in degrading the image for
telescopes larger than about 10 cm. Compensating for this
phenomenon using adaptive optics or placing the telescope
above the atmosphere improve the situation).
Because the actual image distance and size are often
unknown (in astronomy usually unknown), we will
deal with angular magnification instead.
The angular magnification is simple the
ratio of the focal lengths of the objective &
So with a telescope of some fixed objective, higher
magnification is just a matter of using small focal length
eyepieces., The magnification is usually described as
magnifying “power”, often just designated with an “X”.
Thus a telescope with a magnification of 100 would be
described as “100 power” or “100 X”.
When using the human eye to observe with a telescope,
care must be paid to how the beam of light enters the eye.
The so-called exit pupil should roughly match that
of the eye. Making it too big directs light outside the
pupil of the eye, so it is wasted. Making it smaller is
done at the cost of a smaller effective objective opening,
and the image is fainter (the light-gathering power of the
eye is wasted).
Up to a limit then, the larger “cone”
the brighter the source. The number often used to describe
this is the f-ratio defined as
If the focal length is 5 times the diameter, the lese
is said to be an f/5 lens. In both astronomical
photography and terrestrial photography, the eye is
replaced by a camera (which may or may not have a lens in
it). The smaller the f-number, the brighter the image
formed on the detector (film, plate, CCD chip, etc).
Getting small f/ requires highly curved lenses, and this
requires the use of multiple lenses of differing shapes
& materials in order to minimize chromatic (and other)
aberration. Every surface that is required costs money to
In order to avoid chromatic aberration, Newton invented
the reflecting telescope. The strengths of reflectors over
avoidance of chromatic aberration
only one surface to shape precisely
the glass need not be Perfect” in its interior
its weight can be supported from the back
The light convergence is done by using a curved surface
for the mirror. If that were all that were use, however,
the eyepiece and the observer’s head would have to be
placed in front of the telescope, blocking the light! So
Newton used a flat secondary mirror to redirect the light
to the side. This design is still called a Newtonian
A spherical mirror will produce noticeable spherical
aberration unless the f-ratio is large. Spherical
aberration is eliminated by using a parabolic mirror, at
the cost of introducing coma. Another way to produce a
better image is to use a curved secondary mirror
designed to remove some of the aberrations of the
objective or primary mirror. The Cassegrain
telescope is one example.
Other designs are possible. Placing a
weak lens in front can help reduce the problems of coma
and spherical aberration without introducing significant
coma, as in the Schmidt-Cassegrain design.
Binoculars are just 2 refracting telescopes joined
side-by-side. They include a pair of special reflecting
prisms in the light path to:
1. shorten the physical length of the tubes holding the
objectives & eyepieces
2. narrow the distance between incoming light paths to
match eye separation
3. invert the inverted image so that it is upright
Cheap imitations (“field glasses”) without the
prisms use Galilean telescopes instead.
A single telescope of this design is called a monocular.
One clever design uses a monocular and magnifier to
make a small microscope!
Film and slide projectors consist of 4 basic
- a lamp (often with a rear reflective mirror to add
- a condenser lens to direct as much light through
the film/slide as possible and form an image of the
filament of the lamp where it won’t be visible
- the film/slide
- the projection lens
The projection lens forms an image of
the film/slide on a screen. The image of the filament,
formed inside the projection lens is so out of focus as
not to be visible.
The design of projection screens is a science of its
own. Screens can be made to reflect the light back in a
number of ways. (There is more to reflective surfaces than
Lambertian and specular reflection!).
The standard “overhead projector” used in
classrooms uses a Fresnel lens as the condenser.
A similar design I used for some
automobile headlights, but the “grooved” surface is
inside. If it were on the outside, it would collect dirt
more easily and be a nightmare to clean!
information about your project. If you are a basic
or advanced member of ScienceProject.com, your
project advisor may prepare the initial
information that you need and enter them in this
section. In any case it is necessary for you to
read additional books, magazines or ask
professionals who might know in order to learn
more about the subject of your research. Keep
track of where you got your information from.
invisible inks: A
you want to find out? Write a statement that
describes what you want to do. Use your
observations and questions to write the statement.
think you know what variables may be involved,
think about ways to change one at a time. If you
change more than one at a time, you will not know
what variable is causing your observation.
Sometimes variables are linked and work together
to cause something. At first, try to choose
variables that you think act independently of each
your gathered information, make an educated guess
about the answer to your question or the result of
an experiment to test each hypothesis. Make a
step-by-step list of what you will do to answer
each question. This list is called an experimental
procedure. For an experiment to give answers you
can trust, it must have a "control." A
control is an additional experimental trial or
run. It is a separate experiment, done exactly
like the others. The only difference is that no
experimental variables are changed. A control is a
neutral "reference point" for comparison
that allows you to see what changing a variable
does by comparing it to not changing anything.
Dependable controls are sometimes very hard to
develop. They can be the hardest part of a
project. Without a control you cannot be sure that
changing the variable causes your observations. A
series of experiments that includes a control is
called a "controlled experiment."
of Experiment (Observation):
are often done in series. A series of experiments
can be done by changing one variable a different
amount each time. A series of experiments is made
up of separate experimental "runs."
During each run you make a measurement of how much
the variable affected the system under study. For
each run, a different amount of change in the
variable is used. This produces a different amount
of response in the system. You measure this
response, or record data, in a table for this
purpose. This is considered "raw data"
since it has not been processed or interpreted
yet. When raw data gets processed mathematically,
for example, it becomes results.
do any calculation for your project, write your
calculations in this section.
what happened. This can be in the form of a table
of processed numerical data, or graphs. It could
also be a written statement of what occurred
It is from
calculations using recorded data that tables and
graphs are made. Studying tables and graphs, we
can see trends that tell us how different
variables cause our observations. Based on these
trends, we can draw conclusions about the system
under study. These conclusions help us confirm or
deny our original hypothesis. Often, mathematical
equations can be made from graphs. These equations
allow us to predict how a change will affect the
system without the need to do additional
experiments. Advanced levels of experimental
science rely heavily on graphical and mathematical
analysis of data. At this level, science becomes
even more interesting and powerful.
the trends in your experimental data and your
experimental observations, try to answer your
original questions. Is your hypothesis correct?
Now is the time to pull together what happened,
and assess the experiments you did.
Questions & Answers:
have learned may allow you to answer other
questions. Many questions are related. Several new
questions may have occurred to you while doing
experiments. You may now be able to understand or
verify things that you discovered when gathering
information for the project. Questions lead to
more questions, which lead to additional
hypothesis that need to be tested.
did not observe anything different than what
happened with your control, the variable you
changed may not affect the system you are
investigating. If you did not observe a
consistent, reproducible trend in your series of
experimental runs there may be experimental errors
affecting your results. The first thing to check
is how you are making your measurements. Is the
measurement method questionable or unreliable?
Maybe you are reading a scale incorrectly, or
maybe the measuring instrument is working
If you determine
that experimental errors are influencing your
results, carefully rethink the design of your
experiments. Review each step of the procedure to
find sources of potential errors. If possible,
have a scientist review the procedure with you.
Sometimes the designer of an experiment can miss