# Light

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.

# $$c = 3.00 \times 10^{8} \small \frac{m}{s}$$ $$c = f \lambda$$

$$c$$ = 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

Light is an electromagnetic waves.

$$c = \lambda f$$ $$\frac{c}{f} = \lambda$$ $$\frac{3.0 \times 10^{8} \, \mathrm{\frac{m}{s}} }{10^{9} \, \mathrm{Hz}} = \lambda$$ $$\lambda = 0.3 \, \mathrm{m}$$
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
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.

solution $$\small \mathrm{\left(\frac{365 \,day}{1 \,year}\right) \left(\frac{24 \,hour}{1 \,day}\right) \left(\frac{60 \,min}{1 \,hour}\right) \left(\frac{60 \,s}{1 \,min}\right)}$$ $$= 3.15 \times 10^{7} \, \mathrm{s}$$
$$v = \frac{\Delta x}{\Delta t}$$ $$\Delta x = v \Delta t$$ $$\Delta x = \left(3 \times 10^{8} \, \mathrm{\tfrac{m}{s}} \right) \left(3.15 \times 10^{7} \, \mathrm{s}\right)$$ $$\Delta x = 9.46 \times 10^{15} \, \mathrm{m}$$
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 $$\Delta x = 4.37 \, \mathrm{ly} \left( \frac{9.46 \times 10^{15} \, \mathrm{m}}{1 \, \mathrm{ly}} \right)$$ $$\Delta x = 4.143 \times 10^{16}\, \mathrm{m}$$

## 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.

region wavelength (m) frequency (Hz)
gamma ray
x-ray 2 × 10-11 1.5 × 1019
ultraviolet 1 × 10-8 3 × 1016
visible light 4 × 10-7 7.5 × 1014
infrared 7.5 × 10-7 4 × 1014
microwave 1 × 10-2 3 × 1010
radio wave 1 3 × 108

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?

Ultraviolet, specifically UVB.

Question: What color in the visible spectrum has the longest wavelength

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?

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.

## 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 colors 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.

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 optical illusions.

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.

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.

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?

red = 1.0
green = 0.4
blue = 0.7

Question: What combination of light sources make the color brown?

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.
• 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?

Green light can be produced by filtering Cyan and Yellow light.

Question: What type of light makes the color black?

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?

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?

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?

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?

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.

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.

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.

Examples of visible thermal radiation: stars, glowing metal, incandescent lights, stove coils, sparks

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?

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)

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?