Light and Color
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Light and Color
Goal: Participants will make explore characteristics of additive color mixing, converging
lenses and spherical mirrors.
Objectives:
1) Participants will mix the primary colors of light and make observations between the
difference between additive and subtractive color mixing
2) Participants will use a magnifying glass as a converging lens and find the focal length
by forming a real image. They will also make observations of this image which will
describe characteristics of the real images of lenses.
3) Participants will use a hemispherical piece of plastic as a concave mirror to model the
eye of a scallop and make real images using a mirror.
Color Mixing Equipment List:
Flashlights, AA batteries, colored filters,
objects to make shadows.???
Real Image Equipment List:
Magnifying lens, white paper, meter stick
Arkansas State Curriculum frameworks:
PS.7.8.7 – Describe how waves travel
through different kinds of media.
PS.7.8.8 – Differentiate among, reflection,
refraction, and absorption of various types
of waves.
Scallop Eye Equipment List:
Clear plastic ornaments, paper clip, meter
stick, tape, white paper
Equipment comes from WalMart, Hobby
Lobby, Ace Hardware, Stage Works (Little
Rock Theatre Supply Co.), and Cynmar.
Background:
The light our eyes can see is only a very small part of the total electromagnetic spectrum
as illustrated in Figure 1 below. Electromagnetic waves also obey the relationship,
f  c , between wavelength, frequency and speed as discussed previously except now
the speed of the wave is the speed of light, 3 10 8 m/s or over 671 million miles per hour
in air or vacuum!
Figure 1 – Electromagnetic Spectrum
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We will focus on electromagnetic waves and specifically the visible part of the spectrum
which we will refer to as “light.” In the visible part of the spectrum our eyes are sensitive
to wavelengths from 700 nanometers (red light) to 400 nanometers (purple light). In
between the color runs through the ROYGBIV spectrum (Red-Orange-Yellow-GreenBlue-Indigo-Violet). Some animals and insects can “see” into the ultraviolet part of the
spectrum (such as bees) or the infrared portion (such as snakes).
A primary color is a color that cannot be created by mixing other colors; however,
primary colors may be mixed to produce other colors. Primary colors are not a physical
but rather a biological concept, based on the physiological response of the human eye to
light. The human eye contains receptors called cones which normally respond to red,
green, and blue light. Although the peak responses of the cones do not occur exactly at
the red, green and blue frequencies, those three colors are chosen as primary because they
provide a wide gamut, making it possible to almost independently stimulate the three
color receptors. To generate optimal color ranges for species other than humans, other
additive primary colors would have to be used.
Adding Primary Colors:
Media that use emitted light and
therefore additive color mixing
(such as television) use the
additive primaries red, green,
and blue. Because of the
response curves of the three
different color receptors in the
human eye, these colors are
optimal in the sense that the
largest range of colors visible by
humans can be generated by
mixing light of those colors.
Red and green, when mixed,
produce shades of yellow or
orange. Mixing green and blue
produces shades of cyan, and mixing red and blue produces shades of purple and
magenta. Mixing equal proportions of the additive primaries results in shades of grey; if
all three colors are mixed at "full-strength", the result is white.
Subtracting Primary Colors using Reflection:
Media that use reflected light and therefore subtractive color mixing (like ink on paper)
use the subtractive primaries yellow, cyan, (often called "blue", though this is a different
hue from the usual additive blue primary), and magenta (likewise sometimes called
"red"). The subtractive color model works best when the surface (or paper) is white, or
close to it. Mixing yellow and cyan produces shades of green; mixing yellow with
magenta produces shades of red, and mixing magenta with cyan produces shades of blue.
In theory, mixing equal amounts of all three pigments should produce shades of grey,
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resulting in black when all three are mixed at "full-strength", but in practice they tend to
produce muddy brown
colors. For this reason, a
fourth "primary" pigment,
black, is often used in
addition to the cyan,
magenta, and yellow colors.
The color space generated is
the so-called CMYK color
space (standing for "Cyan,
Magenta, Yellow, and Key").
In practice, mixing actual
medium such as paint tends
to be less precise. Brighter,
or more specific colors can
be created using natural pigments instead of mixing, and natural properties of pigments
can interfere with the mixing. For example, mixing black and yellow in acrylic creates
green - something which would not happen if the mixing process were perfectly
subtractive. Also, in the subtractive model, adding white to any color should not change
the color at all (since white does not subtract any color) - yet again, in practice, mixing
white with other pigments does alter their coloration.
Subtracting Primary Colors using Filters:
Subtractive color mixing is employed with paints and pigments, in contrast with additive
color mixing with colored lights for spotlighting and theatrical lighting. Subtractive color
mixing can be demonstrated with colored filters, which may be constructed with colored
glass or plastics in which a suitable dye has been dissolved. Such filters absorb a range of
light wavelengths, and the color of the filter is the color of light that is transmitted by the
filter. The most frequently used primary colors for subtractive color mixing are cyan,
magenta and yellow. Filters act by selective absorption, and the action of the idealized
primary filters above is illustrated in terms of the filter's effect on white light composed
of the additive primary colors red, green and blue. Note that two primary filters in
succession can be used to produce each of the additive primary colors. Figure 2 on the
next page illustrates the process of subtractive color mixing using filters.a
a
This discussion and illustration comes from the HyperPhysics website:
http://hyperphysics.phy-astr.gsu.edu/Hbase/hph.html
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Figure 2 – Subtractive color mixing using filters
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Light can also reflect off a surface or refract upon entering (or leaving) a material. For
these phenomena we can consider the light as a straight arrow which we will refer to as a
ray of light. These rays obey the rules of geometry and trigonometry which is why this
study of light is sometimes referred to as geometrical optics.
Reflection: Light rays can reflect off surfaces. The type of surface influences the nature
of the reflected light. If the surface is smooth and doesn’t absorb the light the reflected
light will be uniformly reflected off the surface as illustrated in Figure 3 below. Reflected
light from a smooth surface is called specular. However, if the surface is rough (even
microscopically rough) the light will be bounced in many directions. Reflected light off a
rough surface is called diffuse. The most familiar example of the distinction between
specular and diffuse reflection would be matte and glossy paints as used in home
painting. Matte paints have a higher proportion of diffuse reflection, while gloss paints
have a greater part of specular reflection. Most objects that one sees are visible due to
diffuse reflection.
Figure 3 - Reflection
The Law of Reflection states that
the angle of incidence must equal
the angle of reflection as measured
from a line perpendicular to the
surface (also known as the
normal). If the surface is smooth
then all the light rays are uniformly
reflected. If the surface is rough the
Law of Reflection is still obeyed
but the reflected rays are sent in
many different directions because
the normal is changing due to the changing shape of the surface. A plane mirror is a
common example of a flat uniform surface from which light can be reflected. The image
of yourself in the mirror is called a virtual image because the rays of light appear to
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come from the other side of the mirror.b The reflecting surface can also be curved and we
will focus on concave and convex mirrors.
Convex Mirrors: A convex mirror, as illustrated in Figure 4, consists of a reflective
surface that is smooth and rounded. Rays of light that strike the reflective curved surface
are bounced off according to the law of reflection. To our eyes these diverging rays seem
to come from a location inside the mirror called the focal point. Images reflected in a
convex mirror are “right-side up” and smaller than the original object. The outside bowl
of a silvered spoon is a good example of a convex mirror even though the spoon isn’t
spherical the convex nature of its shape illustrates the same principle. Convex mirrors are
used at the intersections of hallways to provide a wide view to avoid collisions. Convex
mirrors cannot form real images because the rays of light never converge or cross.
Convex Mirror Ray Diagram
Reflective Spoon
Figure 4 – Convex Mirror
Concave Mirrors: A convex mirror, illustrated in Figure 5, consists of a curved
reflective surface that bows inward. Concave mirrors are a bit more complicated than
convex mirrors but it also works using the law of reflection. If an object is placed very
close to the concave mirror the reflected image will look like an enlarged (and slightly
warped but right-side-up) version of a reflection from a flat mirror. The reflected light
appears to come from an object inside the mirror and hence this image is also called a
virtual image. An example of a concave mirror used this way is a makeup or shaving
mirror. If an object is placed at the focal point for the mirror the light rays bounce off the
mirrored surface and leave parallel to each other. Parallel rays never cross so no image is
formed. By increasing the distance between the makeup or shaving mirror and your face
This “other world” aspect of mirrors is often used in art or literature – Alice in Wonderland being a prime
example!
b
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you will eventually find that the reflected image goes blurry and disappears. This is the
focal point! If you continue to increase the distance between yourself and the mirror the
image you see in the mirror will become upside-down and slightly smaller. When the
object is farther away than the focal point from the mirror a real image can be formed
because the rays of light actually cross on the object’s side of the mirror. Anytime rays of
light converge or cross an image can be formed on screen, film, or retina!
Convex Mirror Ray Diagram
Concave Mirror
Concave Mirror
(Object outside focal length.)
(Object inside focal length.)
Figure 5 – Concave Mirror
Light can also refract or bend as it goes from one material into another. Figure 6
illustrates an incident ray approaching a boundary between two mediums such as air and
glass (or air and water). If the media is transparent the ray will primarily be transmitted
into the second media while a little bit will be reflected at the boundary. This is also true
if the incident ray starts in the lower media and refracts into the upper media! The angle
of incidence is the angle measured from the normal (or perpendicular) to the two media
and the incident ray while the angle of refraction is measured between the normal and the
refracted ray. The reflected ray obeys the law of reflection as stated earlier. The Law of
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Refraction (also known as Snell’s Law) states that the angle of incidence and the angle
of refraction are related by the formula, n1 sin 1  n2 sin  2 , where the n’s are the index
of refraction for the media and the subscripts denote media 1 or 2 as in the figure. For
vacuum (and air) the index of refraction is 1.0 while for water it is 1.33 and for glass it is
typically 1.5. The index of refraction is simply the ratio of the speed of light in vacuum to
the speed of light in the medium, or n  c / vmedium . The speed of light is slower in objects
and so the index of refraction is a number greater than or equal to one.
Figure 6 – Refracting Light Rays
The Prism: The angle of refraction actually does
depend on the wavelength (or color) of the light.
This is how a prism can cause white light to spread
into its composite colors (a process known as
dispersion). The different colors have a slightly
different index of refraction (a different speed for
each color!) and so the colors are refracted to
different angles. This initial dispersion is enhanced
when the colors reach the other side of the prism
and are refracted again when propagating out into
the air. A rainbow is another example of light
dispersion via refraction.c
The Romantic poet John Keats is said to have disparaged Isaac Newton’s “unweaving the rainbow by
reducing it to a prism.” In Keats opinion the mystery and beauty of the rainbow was somehow diminished
by understanding how it forms. To a scientist, the simple explanation only adds to the rainbow’s beauty. Of
course Alexander Pope’s couplet honors Newton: “Nature and Nature’s laws lay hid in night; God said, Let
Newton be! and all was light.”
c
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A lens is an optical device that has a one or two curved surfaces that allows light to be
refracted. We will focus on only one type of lens - the double convex lens as illustrated in
Figure 7 below. Parallel rays of light striking the lens are refracted according the Snell’s
Law, however, because the glass is curved like a sphere there will be a point at which the
rays are converged, this is called the focal point.
Figure 7 – Double-convex lens
A double-convex lens can form real and virtual images depending on the location of the
object with respect to the lens’ focal point, see Figure 8. When forming a real image the
rays of light from the object are focused on the other side of the lens and can form an
image on a screen, film, or retina. Your eyeball contains a lens that helps to focus the
light onto the retina at the back of your eyeball. The retina contains the color-sensitive
cells that send signals to your brain via the optic nerve. Eye glasses, contacts or surgery
may be needed to aid the eye in forming a clear image on the retina. Lenses in a camera
or telescope also form real images although the system of optical elements inside is more
complicated than a single lens. Note that the image is up-side-down and smaller than the
object. To form a virtual image the object must be placed between the lens and its focal
point. In this configuration the rays of light appear to originate at a location on the other
side of the lens. The image formed in this way is a right-side-up magnified version of the
original object. A common example of a double-convex lens used in this way is a
magnifying glass.
You may notice that the rays of light depicted on Figure 8 appear to only refract once at
the center of the lens (called the lens plane) rather than twice at each curved edge. These
illustrations are depicting the thin-lens approximation that proposes that the two
refractions of a thin lens may be approximated by a single refraction at the center of the
lens. The thin-lens approximation results in a simple equation that can be used to describe
the location of an image given the object’s location and the focal length of the lens. This
equation is,
1
1
1
1 1 1
or   .


object distance image distance focal length
s s'
f
The image orientation and its magnification are given by the relationship,
image distance
s'
or m   .
m
s
object distance
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Double-convex lens forming a real image.
Double-convex lens forming a virtual image.
Figure 8 – Real and Virtual images formed by double-convex lens.
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Color Mixing Activity:
The filter paper provided in this activity
will allow you to mix the primary colors:
red, green and blue. The white light from
the flash light bulbs shines through the
filter paper resulting in colors that are
predominately red, green or blue but these
are not single unique frequencies of light.
Rather the filter paper will transmit light
over a range. Figure 9 below displays the
transmission characteristics of this brandd
of filter paper. It will be important to note
these characteristics when doing color
mixing activities – the filter paper isn’t
perfect! Note that the blue filter paper will
allow transmission of some red light
whereas the red filter paper will primarily
only let red light through.
Blue
Green
Figure 9 – Filter paper characteristics
Red
1) Darken the room and use the flashlights to perform the following additive color mixing
procedures on a white sheet of paper or a white ceiling tile.
a) Bring the Red and Blue light spots together until they partially overlap. What
color is made?
b) Bring the Red and Green light spots together until they partially overlap. What
color is made?
c) Bring the Green and Blue light spots together until they partially overlap. What
color is made?
d) Bring all three light spots together. What color is made?
2) Examine the screen of a TV or computer monitor with the magnifying glass. You
should see very tiny pixels and if your eyes are very good you can distinguish the red,
d
Roscolux filter paper. Blue = Storaro Azure #2006, Green = Kelly Green #94, and Red = Medium Red
#27
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blue and green segments of the pixels. To get an even better view dip your finger tip in
water and place a drop on the screen.e What do you observe? Television sets and
computer monitors create colors through spatial partitive mixing.f Older TV sets use
electron beams to excite phosphrous pixels on the inside of the screen while modern LCD
(liquid crystal displays) screens use a different methodg to generate the color but the end
result is the same. The individual small pixels of an image are too small for your eye to
resolve and when the screen is viewed from a distance the image appears continuous. See
Figure 10 for an extreme close up of an LCD screen’s pixels.
Figure 10 – LCD pixels from howstuffworks.com
3) Open Figure 11 from the file on the computer desktop. Use the wide pieces of colored
filter paper to do the following subtractive color filtering. To enhance the effects you may
need to roll the filter paper so that the light passes through it multiple times.
a) Hold the red filter up to the screen and focus on the primary colors. What
colors are transmitted? Does this make sense when comparing to Figure 9? Repeat
for the green and blue filter.
b) Hold the red filter paper up to the screen and focus on the yellow, cyan and
magenta colors. Why does the yellow and magenta colors look red? What
happened to cyan?
c) Hold the green filer paper up to the screen and focus on the yellow, cyan and
magenta colors. Describe what happens to yellow, cyan and magenta.
d) Repeat for the blue filter paper and describe what happens to yellow, cyan and
magenta.
The water drop’s index of refraction and its curvature act as a powerful magnifying glass. In fact, Antony
van Leeuwenhoek (1632-1723) a Dutch scientist made the first simple microscope using a tiny drop of
glass. With this apparatus he was the first to explore the microscopic world of biology!
f
Spatial partitive mixing is a form of additive mixing that is achieved by placing small light sources
sufficiently close enough that your eyes cannot see them separately but “blends” them together; in
other words, your eye cannot “resolve” the individual lights. The concept of spatial partitive mixing
was used by the French artist Georges-Pierre Seurat (1859-1891), who created colored paintings in
the late 19th century by dabbing small bits of paint onto canvas; the method is called “pointillism.”
A person standing very close to the painting sees a seemingly random pattern of colored dots that
appear to merge as the person moves farther away.
g
The liquid crystals in the display actually act as light filters. Back lit displays (as in laptops) use
fluorescent white lights behind the screen which is filtered by the LCD pixel. The pixel is turned on or off
by voltage signals from the computer. A side effect of the light transmission through the LCD is that the
light become polarized. Polarized light has all the light waves wiggling in the same plane. Observe an
LCD screen through a polarizing filter to see this effect.
e
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Figure 11 – Color mixing graphic
Lens and Mirror Activity:
We’ll begin with the double-convex lens.
1) Darken the room with the door open
hold the lens between the door and a white
sheet of paper. The paper will act as a
screen to form an image. Move the lens
toward or away from the paper until a
clear image appears on the paper. You
should see something similar to the photo
below. What do you observe about the
image with respect to the original object?
2) Flip the lens around without changing its
position with respect to the screen. Does the
image change? Why or why not?
3) You can determine the lens’ focal length by measuring the distance of the object to the
lens, s, and the distance from the lens to the image, s’, and using the thin-lens formula,
1
1
1
1 1 1


or   .
object distance image distance focal length
s s'
f
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What is the lens’ focal length? Another method to determine the focal length would be to
focus the sun’s light to a point. The object distance is essentially infinite and so we can
say that the image distance equals the focal length.
4) What is the magnification of the image? Recall that the magnification is defined as
m
image distance
s'
or m   .
s
object distance
The minus sign signifies that the image is inverted. You can measure the height of the
object (the door frame) and the height of the image with the meter stick and also compute
the magnification as,
image height
m
object height
Are these two measures of the magnification the same? What significance is a
magnification less than one or greater than one? Note: For an inverted image the image
height is negative.
5) The image on the screen is a real image because the light rays converge and cross in
the plane of the screen. This is similar to how your eye works. The light enters the eye
and the lens focuses it on the retina. We will do an activity devoted to the eye later.
6) Predict what will happen when you block half of the lens with a piece of cardboard.
Will the image be cut in half? Try this and explain the results.
7) On the sheet of paper draw a 2cm tall stick figure. Illuminate the figure with one
flashlight and use the lens as a magnifying glass by looking into the glass. Position the
lens until the image you see is crisp. Describe the nature of the image – is it inverted? Is it
larger or smaller than the original drawing?
8) Measure the distance from the paper to the lens when the image is crisp. Is this greater
than or less than the distance from the lens to the focal point? For the lens to work as a
magnifying glass the object must be between the lens and focal point.
9) You can use the meter stick to measure the image height in the lens by holding the
stick against the glass. What is the magnification of the stick figure? Is it greater than or
less than one? Is the image a real or virtual image?
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Spherical mirrors are common as make up (or shaving mirrors) or as security (or safety)
mirrors. The clear half Christmas tree ball will act as a spherical mirror even though it is
transparent. The plastic is reflective enough that a small amount of light will be reflected
to the mirror’s focal point which is given by,
R
f  ,
2
where R is the radius of the spherical mirror. The scallop is an interesting biological
example of an animal using a mirror as a means of focusing light on its retina.h Scallops
have usually 40–60 small (1 mm) rather beautiful eyes peeping out between the tentacles
of the mantle that protects the gap between the two shells. The eyes point in every
direction. The scallop’s eye has a single chamber. There is a lens of sorts and behind this
a thick two layered retina filling the space between the lens and the back of the eye. See
Figure 12 which displays photographs and illustrations from the paper referenced in
footnote h.
Figure 12 – Scallop eyes (left) and model of scallop eye (right).
The back of the scallop’s eye is spherical (with radius r ≈ 410 μm) and lined with a
reflecting mirror, the argentea, so named for its silvery appearance. Natural mirrors are
not actually metallic, but are made of multilayers of material with alternating high and
low refractive indices which produce significant reflection as a result of interference.
Spherical concave mirrors form images on the same side of the reflecting surface as the
object, and they have a focal length f equal to half the radius of curvature, f = R/2. This
means that the image of a distant object will be situated half a radius of curvature in front
This activity is from the paper “The scallop’s eye – a concave mirror in the context of biology,” by
Giuseppe Colicchia, Christine Waltner, Martin Hopf and Hartmut Wiesner published in the journal Physics
Education, Vol 44, issue 2, March 2009.
h
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of the mirror. The reflecting argentea forms an image just below the back surface of the
lens; this is the region occupied by the photo-receptive parts of the retina. Thus this is an
eye based primarily on a mirror, not a lens. In the scallop’s eye the focal point is actually
a little nearer to the mirror than it would be without a lens, because the lens slightly
converges the light. One might ask why this eye has a lens at all. The probable function
of the dome-shaped lens is to correct the spherical aberration of the mirror. Just like
spherical refracting surfaces, concave mirrors suffer from spherical aberration (overfocusing of rays at a distance from the axis). The eye of a scallop is a very efficient light
collecting system.
To study the scallop’s eye it is helpful to have a model. Figure 13 illustrates the
construction of a model eye based upon the scallop. A paper clip acts to support a white
paper “retina” at the focal plane for the spherical mirror. The eye can form a crude image
of a distant object as illustrated in the Figure. Note: The authors show a color image that
is formed, Kim and I were unable to get as crisp of an image so we recommend using the
bold black arrow which should be on your computer. The sharp contrast between the
white and black lines makes a clear image on the paper retina.
Figure 13 – Scallop eye model (left) and image formation (right)
1) Take the clear half Christmas ornament ball and fashion a paper retina that is an inch
or so wide. Attach it to the paper clip and bend the paper clip into a small handle.
2) Hold the ball with the open side facing the black arrow on the computer screen.
Position the paper retina between the center of the ball and the inside edge until a clear
image is formed on the paper. Describe the image. Is it inverted? Is it larger or smaller
than the object? Is it a real or virtual image?