# Light

## Light as an Electromagnetic Wave

When 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 objects approach the speed of light strange things occur. The object's passage of time slows and its mass increases.

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, s⁻¹]
$$\lambda$$ = 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 103 m 3 x 105 Hz 2 x 10-28 J
microwave 10-2 m 3 x 1010 Hz 2 x 10-23 J
infrared 10-5 m 3 x 1013 Hz 2 x 10-20 J
visible light 0.5 x 10-6 m 6 x 1014 Hz 4 x 10-19 J
ultraviolet 10-8 m 3 x 1016 Hz 2 x 10-17 J
x-rays 10-10 m 3 x 1018 Hz 2 x 10-15 J
gamma rays 10-12 m 3 x 1020 Hz 2 x 10-13 J

Human eyes can only detect 3 narrow ranges of color: red, green, and blue. Our brains actually invent colors that don't exist to describe the experience of multiple colors at once, like pink, cyan, or white.

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Hydrogen gas 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.

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

Non-ionizing radiation is generally below 10eV (1.60 x 10-18 J). It doesn't have enough energy to cause cellular damage by breaking chemical bonds.
E-M Regions: radio waves, microwaves, infrared, visible light

Ionizing radiation is generally above 10eV (1.60 x 10-18 J). It can potentially ionize an atom and break chemical bonds. Breaking chemical bonds can cause cell death and cancer.
E-M Regions: ultraviolet, x-ray, gamma-ray

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

 Click to Run
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 at 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.

Light is produced when charged particles move. As a material heats up the atoms move and vibrate at a range of speeds. This produces photons at a range of frequencies. Because the random speeds of hot particles are unevenly distributed the light has a sharp drop off at higher frequencies and a long tail down to zero.

Everything gives off light of some frequency. People give off frequencies centered on the infrared from their body heat. Hot materials start to emit a noticeable amount of visible light above about 500°C.

Examples of visible blackbody radiation: stars, glowing metal, incandescent lights, the yellow part of fire (not the blue), stove coils, sparks

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.