Margaret M. Loos
(figure available in print form)
PURPOSE:
To learn the various types of lenses that are used, their diameters, focal points, f/value, and characteristic refraction patterns. To use units in both metric and English systems.
MATERIALS:
graduated cylinders, water, various lenses, rulers with markings in both systems, light sources we have constructed, (sample in institute kit,) envelopes for the lenses with the correct information about each lens. (These come with the lenses in the kit available at the institute.)
PROCEDURES:
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A. 1. Partially fill your graduated cylinder with water. Draw a sketch of the top of the water line. This shape is called a meniscus. Examine your lenses to see if any are in this shape.
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2. When you find it place this meniscus lens (now to be referred to as Lens #1) in your Shoebox/light source which is lying on its side. On the data table provided describe the image or images in the lens. Is it single or double? At what distance is the image most clear when you look at some letters on a page of print. Record that distance as the focal length. Please record in both inches and millimeters. Are the letters inverted backwards or normal?
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B. 1. Find a lens that is flat on one side and curves outward on the other side. This lens is called plano-convex.
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2. Repeat parts of procedure 2 above and record information.
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C. Repeat with a lens that is straight on one side and curves in on the other. Plano-concave. What is different about this image?
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D. Repeat with lens that curves out on both sides. This is Biconvex.
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E. Repeat with lens that curves in on both sides. This is Biconcave.
TABLE OF INFORMATION ON LENSES
Type of Lens
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Image
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Single?
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Double?
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Normal?
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Diameter?
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Focal Length?
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F Value
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F Value = Focal Length Divided by Diameter
Additional questions
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1. Which lens is closest to those in my old glasses?
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2. Return your lenses to the envelop with the correct information about type of lenses, diameter and focal length.
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3. What do you think PCV stands for?
PCX
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What do you think DCV stands for?
DCX
LENSES
:
After
we have done the lab on lenses, students will draw these diagrams in their notebooks and label them and add a few notes. They may also peruse the manual and “play” with them and the optical bench and optical bench manual. One thing they may do is project an image of the writing on top of a light bulb on the ceiling with one of the larger positive lenses, thus seeing the principle of the overhead projector we have used previously in class. We will emphasize the difference between a negative, or divergent, lens which can not by itself project an image, and a convergent, or positive, lens which can project an image.
The designations of the simple lenses are:
(figure available in print form)
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Further drawings should be made by the students showing the way light rays are bent by these
simple
lenses
. Simple lenses are made from a single piece of glass and are used as magnifiers or condensers.
(figure available in print form)
(figure available in print form)
Meniscus Lenses
Meniscus lenses are convex-concave. If the outer curve is sharper than the inward, the lens has a positive focal length and magnifies. If the inward curve is greater, it has a negative focal length and acts as a reducer.
(Drawings courtesy of Edmund Scientific Company, Barrington, NJ) Since simple lenses are made from one piece of glass, they are taken from a surface which is part of a sphere. There are aberrations, or unwanted effects, in the refraction. That is also why we can buy second lenses at a reasonable price. Many of our glasses are made up of more than one lens and these multilens glasses may also have aberrations, so designers of lenses are in business to prepare a lens for any given function or correction by minimizing the aberration within the restrictions of cost, size, position, loss of light, etc.
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The
focal
point
, we may have figured out by now, is the lens-to-screen distance for the image of a distant object. The greater lens power, the greater is the concentration power of the lens. It is the reciprocal or l/f of the focal length.
In optics, a lens is defined as a device for forming an image, real or virtual, by the refraction of light. A real image is one which is where it appears to be and can be cast upon a screen. A virtual image is one such as we see in a mirror. It is not where it appears to be and it can not be cast upon a screen. Our single lenses are not good enough for most technologies. It is necessary to mount several lens elements, some convex, some concave, some of dense, high refractive and high dispersive glass, others low refractive or dispersive.
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Lens blanks are ground by substances like carborundum, a very hard form of carbon, or curve generators equipped with diamond tools. Single vision lenses are usually in a meniscus (like the curve on top of water in a narrow tube) shape, the lens being very thin. For astigmatism, the lens is usually toric (like the shape of a section of an automobile tire). This gives two radii instead of one.
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Ben Franklin is credited with coming up with the idea of combining a lower half lens for reading, and the top for distance . . . bi-focals. Now, lens designers either fuse two lenses or polish two different surfaces of the same lens in different ways. Of course, our students are familiar with the newer, very thin shell-like lenses that fit closely over the cornea of the eye. Hard or soft, these are contact lenses. They are usually molded in plastic material and then formed by heat and pressure to the exact shape of the wearer’s eye. In this day and age, it seems almost all problems of vision can be helped. It’s hard to remember that myopia might have caused hunters of early civilizations to lose their ability to hunt, let alone the limitations placed on the elderly without a means of preserving their sight.
ACTIVITY
: Discussion of the limitations on students who need glasses in the classroom and don’t have them or don’t choose to use them. Perhaps some students would share the difference in perception, before and after, they started using glasses. (At least every student in my class is aware of my limitations without my glasses.) My own contribution would be to make the class aware that even they will need glasses at about the age of forty to make up for the failings of an “old-eye” problem.
The microscope and telescope present different requirements. For instance, the maximum useful magnification cannot extend beyond the limits of 30 times to 2000 times the size because the resolution, or clarity, is limited by the nature of light itself. For if wave motion comes upon very small objects, it bends around them (diffraction) and makes the very small object invisible. In order to get the degree of resolution required some microscopes have objectives with as many as fourteen lenses.
In order to study microscopes and telescopes we must also become familiar with the workings of a mirror. We have mentioned the virtual image that we perceive in a mirror. Mirrors, of course, do not refract, they reflect. That is, if an object is placed in front of a mirror, for every point (we’ll call it P) light rays leave these points, fall on a mirror, and reflect in the same order in which they approach the mirror. The observer gets the impression that the object P is at the point P’—behind the mirror and the order of the rays is reversed. We are so familiar with looking in a mirror that we may have to be reminded that they are indeed in reverse order by holding up a sign to see that the image has reversed the letters. Therefore, the image observed in a plane mirror is as far back of the mirror as the object is in front of the mirror and it appears to be reversed from left to right. All rays would follow the law of reflection which says that the angle of incidence is equal to the angle of reflection.
ACTIVITY
: Diagram of a reflected letter.
Examination of plane mirrors, making angles with mirrors, sequences of reflections, convex and concave mirrors.
ACTIVITY
: Labeling of the structures in a microscope and a telescope.
Comparison with Hooke’s microscope and Galileo’s telescope. Attempt to duplicate Galileo’s telescope with our equipment.
It may come as a surprise to students that reflecting telescopes have many advantages over refracting telescopes. First, the difference is, of course, based on the fact that reflecting telescopes principally employ mirrors and refracting telescopes employ lenses. Some advantages of reflecting over refracting are:
1. Refractors need longer tubes
2. Reflectors can have larger diameters
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3. Refractors require lenses with two perfectly ground sides and reflectors’ mirrors require only one perfectly ground side.