Class notes by RE-SEED Leader - Alex Vanderburgh

RESEED Notes - Class 10 - 11 Sep 2001 - Optics - Framingham 10-1
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"Light" - A physical event, and also a human perception.
Just a few words on "theory". All of us are aware of "rays" or
"beams" of light. As children, a flashlight was a wonderful toy.
(Especially on a foggy night!) One of the early theories was that a
ray of light was "corpuscular". It was made of very fast, very tiny
particles. Then the "better" theory was that it was an
"electromagnetic wave". Now you hear BOTH! The corpuscles are now
"photons" (energy particles), but somehow the "wave equations" still
apply. [Do photons have mass?]
Theories of light are interesting, but probably too complex for
grade school students. Fortunately we can use light very well,
concentrating on what we can do or make, without much theory as to
what it "is". We will picture light as "rays" - a flashlight is a
"ray gun". We assume a ray is straight, and that the air or whatever
the ray is passing through is uniform. We can measure the length of
rays, and perhaps we can find a photocell or light meter that would
be interesting. [I have a problem here, in that I can not explain
how it works.]
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Reflection: [It's all done with mirrors! ]
A ray of light striking a mirror bounces off as a billiard ball
"reflects" off a pool table cushion. The angle of reflection is
equal to the angle of incidence. [In Optics, these angles are
measured from a line perpendicular to the mirror surface.]
In ordinary life, we see things by the light they reflect. This
type of reflection is called "diffuse". The rays are scattered in
all directions, and often only a certain color is reflected. Mirror
reflection is called "specular". [A speculum is a metallic mirror
used in optical instruments.] If you shine a spotlight on a perfect
mirror, the mirror will look "black" except at the exact angle where
you would see the image of the spotlight. If you pulverize a glass
mirror, you get white sand. When you shine the spotlight on the
sand, the reflection is diffuse. You can see the spot from any angle.
Optical instruments are made to very precise measurements - way
smaller than the average person uses. The typical unit of length is
the Angstrom (0.000,000,000,1 meter, or 0.1 nanometer). Most atoms
are about 1 or 2 angstroms wide. An optically "flat" mirror is flat
to a few Angstroms.
But be of good cheer. There is a lot that can be observed
without higher math or complex theory. With two mirrors you can make
a periscope! With three, a kaleidoscope! I recommend making your
periscope in two pieces so that you can rotate one end with respect
to the other. This way you can look around a corner or directly
behind. Try it! You may be a bit surprised. Be sure to try it over
your head as well as around a corner. Ray diagrams will help show
what is happening.
A kaleidoscope can be made by taping three long rectangular
mirrors as a tube with the mirror sides inside. When you look
through the tube at something, and rotate the tube, you get inter-
esting reflections. Often they are made with a container of glass
pieces that can be rotated instead of the tube to change the
pattern.
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Refraction - "Bending" of light rays by prisms and lenses...
Unexpected things happen when a ray of light encounters a
different medium. For example air/water or air/glass. Straight on,
there is no mystery. There is some reflection at the boundary, but
the rest of the ray goes right in. If the incident ray is at an
angle, the internal ray is not in line. It has been "bent" a little
to a new direction. This bending is called refraction. Each material
has an "index of refraction" (a number you can look up) that can be
used to calculate how much the "bending" will be. The ray inside is
called the "refracted" ray. You can see that it changes with the
angle of incidence. If the piece of glass is an accurately made
rectangle, the ray will come out through a parallel surface and gets
bent back - parallel to the original ray. However, if the angle of
incidence (going out) exceeds a certain amount, all of the ray is
reflected back inside. [Note that the performance of "light pipes"
or "fibre optics" depends on this.]

Color - Especially the "color" of Sunlight 10-2
It turns out that the "bending" of light is different for
different colors. A ray of sunlight passing through a triangle
shaped glass (a prism) will be spread out into a rainbow of colors.
We see red, orange, yellow, green, blue, and violet. [With special
devices, we can detect a color (called infra-red) just before the red
and one (called ultra-violet) just after the violet . The incident
ray from the sun looks "white".
A rainbow is more easily seen when you look at rain with the sun
behind you. From an airplane, it is a complete circle with the shadow
of the airplane at the center. A ray of sunlight enters the drops at
such an angle that it reflects internally, and exits the drop at an
angle of 42 degrees from the incident ray. But the bending is
different for each color! Sometimes the angle is such that it bounces
twice internally. That produces another rainbow with the order of
colors reversed! The sky between the two rainbows is darker. (Some
light rays never get back to you.)
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mirrors 1 Lg. 3 sm. Spotlight Glossy paper
sand balls 2 in. gravel
plate protractor ray box
slit flashlight cover poster bd. clay
candle & matches plastic cup plexiglass
box for candle illusion Mineral Oil
Piece of quartz prisms magnifier


Demo 1 - Spotlight and various kinds of paper, and wet sand.
Demo 3 - Beach ball vs ping-pong ball on a gravel surface.
Demo 4 - "Law of Reflection" via ray box and mirror.
Demo 5 - Magic - A candle burning under water
Demo 6 - Refraction: Light rays bend at the border between two media.
Demo 7 - Quartz disappears in mineral oil. [Same index!]
Demo 8 - Prisms and ray box.
Demo 9 - Thin lens law. A magnifier (convex lens) can project an
image. Half a magnifier does the same, but dimmer.
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Errata: - Page 110 - Last line - Change refraction to reflection.

Page 112 - Figure 3 - Change asphalt to grass.

" " - line 8 - change mineral water to mineral oil.
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Snell's Law - Index of refraction
The difference in refraction we observe when a different color
is used, is not included in the equation. For precise work you can
look up an index for each color. It turns out that the variation is
quite small. The index is 1.513 for red to 1.532 for violet for air
to "crown" glass. About one percent deviation from the average.
[Glass varies from 1.5 to 1.9. water is 1.33, for fused quartz and
mineral oil(oleic acid), it is 1.46.]

So what is the formula? Basically it is Snell's law:

The ratio of the Sine of the angle of incidence
to the Sine of the angle of refraction is constant.
[It is not changed when the angle of incidence is
changed.]

[This ratio is called the "Index of Refraction"] 10-3

But what is it in plain English? ("Sine" is not a common
word.) It turns out that a drawing may make it easier. If you
draw a unit circle centered where the ray hits the glass, you
can see that the bent ray (inside the glass) hits the circle
closer to the vertical than the incident ray did.
We need to measure these two horizontal distances. (From the
intersection of incident ray and circle to the vertical line,
and the corresponding distance for the refracted ray.) The ratio
of these two distances was found to be constant as the angle of
incidence is changed! This constant is the index of refraction.

If you know Trigonometry, you will recognize these lines as the
"sine" of the angles, since we drew the circle with a radius of
one.

The "Index of Refraction" is considered to be a physical property
of the material - like "boiling point"...etc. Most tables show the
index relative to "air". It is slightly different in a vacuum; the
difference shows up in the fourth decimal place. [1.50044 for vacuum
to glass vs 1.50000 for air to glass.] For most cases the values for
air are sufficient.

There must be a way to relate the index of refraction to the
speed of light in the different media. My guess is that it is so
obvious that it can just be stated: The index of refraction is,
of course, the ratio of the speed of light in a vacuum to the speed
of light in some medium - like glass. [The index for air is 1.00029.]
If you find out more about this, please let me know. Does the fact
that light is bent imply a difference in the velocity of light, or
does the difference in velocity predict that a beam will be bent? I
prefer the former since I can measure the bending.

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A question for review - probably belongs in chapter 7.

Teachers sometimes feel that "trick" questions are extra
revealing and therefore good instruction. Sometimes they reveal bad
teaching! Our kids are getting bad information from some texts in
use. Here is an example that may actually be useful. The book says
that the mass of the moon is 1/6 that of the earth. Actually it is
the gravitational force of the moon on an object on its surface, that
is 1/6 what it would be for that object on Earth. We are accustomed
to thinking that mass and weight are almost interchangeable. When we
compare planets, often the Mass of the planet is quoted, and then the
weight of a typical person on each planet is compared. Note that the
moon's mass is about 1/81 that of Earth. This looks wrong! We all
know that we would weigh 1/6 - not 1/81!

The books should calculate the weights - not just give them. Then it
would be clear that in addition to mass, you must also figure in the
square of the distance! The moon is a lot smaller. Standing on the
moon you are a lot closer to the center of its mass! Note also that
the force varies as the square of the distance. If you double the
distance to the center of mass of your planet, your weight decreases
by a factor of four! You will have to go out about 4,640 kilometers
from the surface of the moon to get to the same distance as the
earth's surface is from its center. Then you will weigh 1/81 as much
as you do at home.

Do you think this would make a good MCAS question?