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Optical Instruments


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 is

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 lenses (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 reading glasses, removing them will allow you to view the microscope properly.

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….

Refracting Telescopes

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 telescope.

Galilean Telescope

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.

Keplerian Telescope

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.

Light-Gathering Power

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).

Angular Magnification

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 & eyepiece:

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”.

Image Brightness

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 make…..

Reflecting Telescopes

In order to avoid chromatic aberration, Newton invented the reflecting telescope. The strengths of reflectors over refractors are:

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 telescope.

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!

Projection Systems

Film and slide projectors consist of 4 basic components:

  1. a lamp (often with a rear reflective mirror to add more light
  2. 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
  3. the film/slide
  4. 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!


Introduction: (Initial Observation)

Introduction: I

Information Gathering:
Gather information about your project. If you are a basic or advanced member of, 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.

Fluorescent invisible inks:

Question/ Purpose:
What do you want to find out? Write a statement that describes what you want to do. Use your observations and questions to write the statement.

Question: What ...

Purpose: The ...

Identify Variables:
When you 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 other.
Based on your gathered information, make an educated guess about the answer to your question or the result of your experiment. 
Experiment Design:
Design 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."

Procedure: Do ...


Materials and Equipment:
Material: The ...
Results of Experiment (Observation):
Experiments 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.
If you do any calculation for your project, write your calculations in this section.

Summery of Results:
Summarize 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 during experiments.

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.

Using 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.
Related Questions & Answers:
What you 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.

Possible Errors:
If you 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 erratically.

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 the obvious.

List of References