The spectrum of light extends far beyond the visible light that our eyes evolved to detect. Cell phones and
Wi-Fi use microwave light to transmit digital information. CT scans use x-ray light to look inside a
person's body. Thermometers use infrared light to read temperature. All of these different types of light
are produced in the same way.
When a charged particle accelerates, its electric field and magnetic field change.
This change propagates as a wave in the electro-magnetic field. The wave is light.
Changes in an electric and magnetic field don't happen immediately. It takes time for changes in an
electromagnetic field to propagate through space. The speed of these changes to the E-M field is the speed
of light.
In this simulation a charged particle follows your mouse. The
white lines show the electric field
from a charged particle.
The ripples in the field lines are light.
A quick acceleration makes high frequency light. Slow acceleration makes low frequency light. You can't
quite make a "sonic boom" with light
because a charged particle can't move faster than the speed that light waves propagate.
The Speed of Light
In 1676 Ole
Rømer estimated that light has a speed by
timing the eclipses of Io, one of Jupiter's moons. He found the speed to be around 220 000 000
m/s. This isn't too far from the value we use today.
We can use the speed of light as the velocity in the wave equation.
\(c\) = speed of light [m/s]
\(f\) = frequency [Hz, 1/s]
\(\lambda\) = wavelength [m]
The speed of light in a vacuum is the fastest possible speed! No object has ever been recorded moving
faster. As objects approach the speed of light their time
dilates and length contracts.
A light wave moves slower in dense media because light induces electric polarization in matter, and the
polarized matter radiates new light that interferes with the original light wave to form a delayed wave.
speed of light
vacuum
air
water
diamond
(m/s)
299 792 458
299 700 000
225 000 000
120 000 000
When we say "the speed of light" we generally mean the vacuum speed.
Example: Find the wavelength of an electromagnetic wave that has a frequency of
109 Hz.
solution
Example: The Sun is 1.50 × 108 km from Earth. How long does it take for the light
from the Sun to reach us?
solution
$$v = \frac{\Delta x}{\Delta t} $$
$$\Delta t = \frac{\Delta x}{v} $$
$$\Delta t = \frac{1.50 \times 10^{8}\times10^{3}\,\mathrm{m}}{3.0 \times 10^{8}\,\mathrm{\frac{m}{s}}} $$
$$\Delta t = 500\, \mathrm{s} $$
$$\Delta t = 8.33 \, \mathrm{min} $$
Example: The center of the Earth is 384 400 km from the center of the Moon. What is the
shortest amount of time it takes light to travel from the Moon to the Earth?
Local Massive Objects Data Table
Planet
mass (kg)
radius (km)
Sun
2.00 × 1030
695 700
Mercury
3.301 × 1023
2440
Venus
4.867 × 1024
6052
Earth
5.972 × 1024
6371
Moon
7.346 × 1022
1737
Mars
6.417 × 1023
3390
Jupiter
1.899 × 1027
70 000
Saturn
5.685 × 1026
58 232
Uranus
8.68 × 1025
25 362
Neptune
1.024 × 1026
24 622
solution
$$\Delta x = 384\,400\,\mathrm{km} - 6371\,\mathrm{km} -1737\,\mathrm{km} = 376\,000\,\mathrm{km}$$
$$v = \frac{\Delta x}{\Delta t} $$
$$\Delta t = \frac{\Delta x}{v} $$
$$\Delta t = \frac{3.76 \times 10^8 \,\mathrm{m}}{3.0 \times 10^8\,\mathrm{\frac{m}{s}}} $$
$$\Delta t = 1.25\, \mathrm{s} $$
A light-year [ly] is a unit of distance. A light year is the distance that light travels
in one year. It is mostly used to measure distances to objects outside the solar system.
Example: How far is one light year in meters?
strategy
$$v = \frac{\Delta x}{\Delta t} $$
The velocity is the speed of light. The time is 1 year. Be sure to convert units.
Example:Alpha Centauri is
the nearest solar system to ours. It is 4.37 light-years away.
How far away in meters is Alpha Centauri?
solution
$$\Delta x = 4.37 \, \mathrm{ly} \left( \frac{9.46 \times 10^{15} \, \mathrm{m}}{1 \, \mathrm{ly}}
\right)$$
$$\Delta x = 4.134 \times 10^{16}\, \mathrm{m}$$
The Electromagnetic Spectrum
Light can be viewed as a spectrum.
The lowest energy, lowest frequency, and longest wavelength are on one end.
The highest energy, highest frequency, and shortest wavelength are on the other.
The electromagnetic spectrum is very loosely divided in these regions based on the source of that
light.
Microwave and radio waves are produced by changing electric current.
Infrared light is mostly produced by the thermal radiation of bodies at room temperature.
Visible light comes from thermal radiation (sunlight), chemical reactions (fire), and numerous technologies
(LED, laser, cathode ray tube, gas discharge lamps).
Ultraviolet light comes from the same sources as visible light, but at a slightly higher frequency that
humans can't see.
X-rays can be produced by accelerating electrons very quickly, like in cathode ray vacuum tubes.
Gamma rays are similar to X-rays, but they are generally distinguished by coming from radioactive decay
instead of electron acceleration.
Question: Hydrogen is the most common element in the universe, making up about 75% of all
normal mass. It floods the universe with light at its signature wavelength of
21 cm. What region of the electromagnetic spectrum
would this light be in?
answer
$$21\, \mathrm{cm} \left(\frac{0.01}{c}\right) = 0.21\, \mathrm{m}$$
$$\text{ 0.21 m is in the microwave}$$
Question: In human skin, vitamin D production occurs when a precursor molecule reacts with
light at wavelengths between 270 and 300 nm. What range of the E-M spectrum includes that wavelength?
answer
Question: What color in the visible spectrum has the longest wavelength
answer
Red has the longest wavelength.
Light slows down in denser media, which causes it to refract.
Refraction causes the various frequencies that make up white light to disperse because each
frequency slows to a different speed.
Question: Use the image to decide what color moves the slowest in glass.
answer
Blue / violet light refracts at
the most extreme angle.
This means that as light passes through glass, blue slows down the most and red the least.
Question: The color of an object is determined by the wavelength of light it reflects.
Which color of visible light has the shortest wavelength?
answer
Violet has the shortest wavelength in the visible spectrum. It has a wavelength of around 380-450
nm.
Color Vision
Our eyes have two types of cells that respond to visible light, rods and cones.
Rods detect visible light with a high sensitivity. Cones specialize in
detecting the wavelength of the light.
Cone cells come in different types that are sensitive to different wavelengths of visible light.
The number of colors receptors has varied as life has evolved. Most birds and reptiles have 4 different
color receptors.
Mammals have 2 color vision, with the exception of primates that have 3
color vision.
Humans are primates, so we mostly have 3 different color receptors, but some color blind humans have 2.
They don't see in black and white, they just have trouble telling the difference between some colors, like
red and green.
Human cones cells respond to 3 overlapping regions on the electromagnetic spectrum.
We can see every color on the rainbow from this
information.
What about colors not on the rainbow?
If multiple cones are activated our brains invent colors to describe the experience, like pink or white.
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Information from our eyes is processed in our
brains to build a guess about what we are seeing.
Our brain's interpretation isn't perfect. We call these mistakes opticalillusions.
One source of confusion comes from similar terms for subtractive and additive colors. Light sources work
by adding color.
Adding more colors of light will bring the color we see closer to white.
This is how computer screens produce a wide gamut of color.
green light +
blue light appear
cyan red light +
blue light appear
magenta red light +
green light appear
yellow red light
+
green light +
blue light appear
white
Pigments, paints, dyes, and filters work by subtracting color. When white light shines on
blue
paint it looks blue because the blue pigment absorbs every color except blue. Adding more pigments will
remove more color and bring the reflected light closer to black, the absence of light.
magenta dye +
yellow dye reflect only
red light cyan dye +
yellow dye reflect only
green light cyan dye +
magenta dye reflect only
blue light cyan dye
+
magenta dye +
yellow dye
reflect
no light
Question: What three colors of light does a TV need to make every color that humans can
experience.
answer
Most televisions can only produce red, green, and blue light. They get the other colors from
different ratios of red, green, and blue.
Question: What three pigments does a printer need to make every color that humans can
experience.
answer
Most printers use a combination of cyan, magenta, yellow, and black.
light
Red
Green
Blue
filter
Cyan
Red
Magenta
Green
Yellow
Blue
Question: What combination of light sources make the color pink?
answer
red = 1.0
green = 0.4
blue = 0.7
Question: What combination of light sources make the color brown?
answer
Brown is tricky. Brown is dark orange, in the same way that grey is dark white.
Orange is red plus a bit of green, and almost no blue.
Making orange look dark depends on context.
Dark orange only looks dark with a bright background.
If you aren't convinced try this:
Make your surroundings completely dark.
(it will only work if the room you are in is super dark)
Click on the brown square to darken the background color of this page.
Wait at least ten seconds for your eyes to adjust.
Look at the brown box again.
Question: A green filter removes red and blue light to leave just green light.
How else could filters turn white light into green light?
answer
Green light can be produced by filtering Cyan and Yellow light.
Question: What type of light makes the color black?
answer
the absence of light
Polarization
Polarization is a property of transverse waves that describes the angle of oscillation. The
polarization can be any angle perpendicular to the direction the wave is moving.
Most light sources are unpolarized. They oscillate a bit in every direction. Light can become polarized
after passing through a polarization filter that only removes the light that oscillates at a certain angle.
A polarization filter that blocks vertical light
will let horizontally polarized light through. Polarization filters are often used in sunglasses or 3-D
movies.
Unpolarized light can also become partially polarized after reflecting off some shiny surfaces. The
reflected light becomes polarized parallel to the surface. For example, a flat road reflects horizontally
polarized light.
Question: What polarization does the Sun produce?
answer
Most light sources, including the Sun, don't produce one polarization. They produce light with
random polarizations.
Although, the refracted blue sunlight from Rayleigh
scattering is polarized towards the Sun.
Question: What classifications of waves can and can't be polarized?
answer
Transverse wave, like light, can be polarized.
Longitudinal waves, like sound, can't be polarized.
(except for sound waves in solids, which can be transverse)
Question: What angle would a polarization filter need to be to block the glare from a
highway road?
answer
A horizontal polarization filter will block the glare from a road.
Question: Imagine looking at sunlight through a horizontal polarization filter and a
vertical polarization filter. What color would you see?
answer
It would just be black, since all the light would be blocked.
If you put a filter at 45° between a horizontal and vertical polarization filter it isn't black due
to a fascinating, but complex, quantum
mechanical interactions.
Thermal Radiation
The particles in all substances move and vibrate in a seemingly random way. Temperature is a measure of the average kinetic energy of
these particles. When the temperature is high there is more motion.
When charged particles accelerate they produce light. This means that as substances get hotter they make
brighter and higher frequency light.
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All matter gives off light due to its temperature. Objects at room temperature give off infrared light.
Materials above 500° C start to emit visible light as well.
The wavelengths given off by thermal radiation reflect the range of particle speeds. Because the speeds are
unevenly distributed the light produced has a sharp drop off at shorter wavelengths and a long tail for
longer wavelengths.
Question: Could a substance at room temperature emit a UV ray from thermal emission?
answer
Yep, but it would be rare.
Question: You see several substances glowing from thermal emission. What color do you
suspect is the highest temperature?
(red, yellow, white, black, pink, green, orange, blue)
answer
hottest to coldest:
blue, white, yellow, orange, red, black
(pink and green are not possible thermal emission colors)
Question: Why is fire blue on the
stove, but normally yellow?
answer
Only a small part of a flame's color comes from thermal radiation.
A flame has a temperature around 1200° C, which would only appear dark red from thermal emission.
Most of a flame's light is released when electrons rearrange during chemical reactions.
The blue light in a flame comes from oxygen chemically reacting with a fuel source.
When fire doesn't have enough oxygen, extra carbon atoms are produced.
These carbon atoms group up into large "soot" particles.
The soot releases yellow light as the carbon breaks and reforms bonds.
Unusual colors like green come from adding impurities to the fire.
For example, when copper is added to fire it releases green light in a process called line emission