# Light

The spectrum of light extends far beyond the visible light that our eyes evolved to detect. Cell phones 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 are light are produced by the mechanism.

When a charged particle moves, its electric field and magnetic field updates to the new position. We call this change in the electric and magnetic field an electromagnetic wave or light!

Try moving around in this simulation to see how the electric field updates as a charged particle moves. The ripples in the field lines are what we call light.

## The Speed of 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.

The speed of light in a vacuum is the fastest possible speed! No object has ever been recorded moving faster. As one approaches the speed of light your experience of space and time warp relative to a nonmoving object.

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]

Light seems to move slower in dense media because the photons of light are being absorbed and emitted by the atoms of the medium.

The speed of light in a vacuum is 3.0 × 10⁸ m/s.
The speed of light in water is 2.3 × 10⁸ m/s.
The speed of light in diamond is 1.2 × 10⁸ m/s.

Example: Find the wavelength of light that has a frequency of 10⁹ Hz.
solution $$c = \lambda f$$ $$\frac{c}{f} = \lambda$$ $$\frac{3.0 \times 10^{8} \frac{m}{s} }{10^{9} \frac{1}{s}} = \lambda$$ $$\lambda = 0.3m$$
Example: The Sun is 1.50x10⁸ km from Earth. How long does it take for the light from the Sun to reach us?
solution $$v = \frac{\Delta x}{\Delta t}$$ $$\Delta t = \frac{\Delta x}{v}$$ $$\Delta t = \frac{1.50 \times 10^{11}}{3.0 \times 10^{8}}$$ $$\Delta t = 500s$$ $$\Delta t = 8.33 min$$

A light-year [ly] is a unit of distance. 1 light year is the distance that light can travel in one year. It is mostly used to measure distances to objects outside the solar system.

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 $$\tiny 4.37 year \left(\frac{365 day}{1 year}\right) \left(\frac{24 hour}{1 day}\right) \left(\frac{60 min}{1 hour}\right) \left(\frac{60 s}{1 min}\right) = 1.378 \times 10^{8} s$$ $$v = \frac{\Delta x}{\Delta t}$$ $$\Delta x = v \Delta t$$ $$\Delta x = \left(3 \times 10^{8}\right) \left(1.378 \times 10^{8}\right)$$ $$\Delta x = 4.143 \times 10^{16}m$$

## 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.

region wavelength frequency energy
radio waves 10 3 m 3 x 10 5 Hz 2 x 10 -28 J
microwave 10 -2 m 3 x 10 10 Hz 2 x 10 -23 J
infrared 10 -5 m 3 x 10 13 Hz 2 x 10 -20 J
visible light 0.5 x 10 -6 m 6 x 10 14 Hz 4 x 10 -19 J
ultraviolet 10 -8 m 3 x 10 16 Hz 2 x 10 -17 J
x-rays 10 -10 m 3 x 10 18 Hz 2 x 10 -15 J
gamma rays 10 -12 m 3 x 10 20 Hz 2 x 10 -13 J
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 21cm. What region of the electromagnetic spectrum would this light be in?
solution $$21cm \left(\frac{0.01}{c}\right) = 0.21m$$

0.21m is a microwave.

In human skin, vitamin D production occurs when the precursor molecule reacts with light at wavelengths between 270 and 300 nm. What range of the E-M spectrum includes that wavelength?
solution

Ultraviolet, specifically UVB.

## Color Vision

Our eyes have two types of cells, called rods and cones, that can detect electro-magnetic waves. Rods detect visible light with a high sensitivity. Cones specialize in detecting the wavelength of the light. From the cones come color vision.

The number of colors that are detectable has varied as life has evolved. Most birds and reptiles have 4 different colors they can detect. Mammals have 2 color vision, with the exception of primates that have 3 color vision.

The colors we can see come from three overlapping regions. We can see every color on the rainbow from just 3 different types of cones. What about colors not on the rainbow? If multiple cones are activated our brains actually invent colors to describe the experience, like pink or white.

Light sources work by adding color.
Pigments and dyes work by subtracting color.

What combination of colors do we call pink light?
solution

Red plus blue light makes pink.

What type of light makes the color black?
solution

the absence of light

Radiation is a wave or particle that transmits energy through space. This includes particles with mass (electrons) and massless particles (photons).

Non-ionizing radiation is generally below 10eV (1.60 x 10 -18 J). This "safe" radiation doesn't have enough energy to cause cellular damage by breaking chemical bonds.

radio waves, microwaves, infrared, visible light

Ionizing radiation is generally above 10eV (1.60 x 10 -18 J). This "unsafe" radiation can potentially ionize an atom and break chemical bonds. Breaking chemical bonds can cause cell death and cancer.

ultraviolet, x-ray, gamma-ray

Try this PhET simulation to see how different molecules interact with different regions of the electromagnetic spectrum.

Greenhouse gasses need to interact with infrared light. Which molecules from the simulation could be greenhouse gasses?
solution CO | CO₂ | H₂O | NO₂ | O₃ all could deflect infrared light as it leaves the earth, preventing the earth from cooling.
Can microwave ovens ionize atoms? Are they dangerous?
solution
Microwave ovens make microwaves. Each microwave photon has an energy around 10 -23 J. This is far below the threshold for ionizing atoms
(1.60 x 10 -18 J).

This means microwaves can heat up things, but they will not directly cause cell damage or cancer.

Cell Phones and Wifi also use microwaves to transmit data. Many studies have been done, but the current evidence indicates that cell phones and wifi don't cause cancer. Since microwaves are so common there continues to be research on this.
Which is more damaging an ultraviolet or gamma-ray photon?
solution

Gamma Rays.
UV is less likely to ionize cells. Gamma-rays have much more energy per photon, but gamma-rays also have higher penetration, so they can pass deeper into the body.

The particles in all substances move and vibrate randomly. Temperature is a measure of the average kinetic energy of these particles. When the temperature is high there is more motion.

When charged particles move they produce light. This means that as substances get hotter they make brighter and higher frequency light.

All matter gives off light due to it's 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, the yellow part of fire (not the blue), 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.

Based on the graph above, estimate the temperature of the sun's surface.
solution

The blackbody spectrum of the sun is centered on visible light. It should be slightly above the 5000K spectrum.

Does this mean that even room temperature materials could emit a UV ray?
solution

Yep, but it would be rare.

Which is the hottest of these materials?
red, yellow, white, black, pink, green, orange, blue
solution

blue!
(pink and green are not even possible colors)

If fire is caused by thermal radiation, why is fire sometimes blue, or yellow, or even green?
solution

Fire has light from both chemical reactions(blue) and thermal radiation (red/yellow). Watch this video for more.