13.1 Nature and Properties of Light

Electromagnetic Waves

Characteristics of Electromagnetic Waves

Electromagnetic waves are waves of oscillating electric and magnetic fields that travel through space. Unlike sound waves, they don't need a medium, which is why sunlight can reach us through the vacuum of space.

Here are the key properties you need to know:

• Wavelength is the distance between two consecutive crests (or troughs) of a wave, measured in meters or nanometers.
• Frequency is the number of complete waves passing a fixed point per second, measured in hertz (Hz).
• Amplitude is the maximum displacement of a wave from its resting position. For light, amplitude relates to brightness.
• The speed of light in a vacuum is constant at approximately $3.0 \times 10^8$ meters per second (299,792,458 m/s to be exact). Every type of electromagnetic wave travels at this speed in a vacuum.

The full range of electromagnetic radiation, from radio waves to gamma rays, is called the electromagnetic spectrum.

Electromagnetic Spectrum Components

The spectrum is organized from longest wavelength (lowest frequency, lowest energy) to shortest wavelength (highest frequency, highest energy):

All of these are the same type of wave. The only difference between a radio wave and a gamma ray is wavelength and frequency.

A helpful memory trick: the order from longest to shortest wavelength goes R-M-I-V-U-X-G (Radio, Micro, Infrared, Visible, Ultraviolet, X-ray, Gamma).

Relationships Between Wave Properties

The core equation connecting wave properties is:

$c = \lambda f$

• $c$ = speed of light ($3.0 \times 10^8$ m/s in a vacuum)
• $\lambda$ (lambda) = wavelength in meters
• $f$ = frequency in hertz

Because $c$ is constant in a vacuum, wavelength and frequency are inversely proportional. If one goes up, the other must come down. A wave with a long wavelength has a low frequency, and a wave with a short wavelength has a high frequency.

Quick example: If a wave has a frequency of $5.0 \times 10^{14}$ Hz, you can find its wavelength by rearranging the equation:

1. Start with $c = \lambda f$
2. Solve for wavelength: $\lambda = \frac{c}{f}$
3. Plug in: $\lambda = \frac{3.0 \times 10^8}{5.0 \times 10^{14}} = 6.0 \times 10^{-7}$ m = 600 nm
4. That's orange light.

Energy also ties into this relationship. Higher-frequency waves carry more energy. That's why gamma rays are dangerous and radio waves are harmless: gamma rays pack far more energy per photon.

Properties of Light

Visible Light Characteristics

Visible light is the narrow band of the electromagnetic spectrum that human eyes can detect, spanning wavelengths from about 380 nm (violet) to 700 nm (red). That's a tiny fraction of the full spectrum.

Different wavelengths correspond to different colors:

• ~700 nm = red (longest visible wavelength, lowest energy)
• ~580 nm = yellow
• ~520 nm = green
• ~450 nm = blue
• ~380 nm = violet (shortest visible wavelength, highest energy)

The order follows the familiar ROY G BIV sequence (red, orange, yellow, green, blue, indigo, violet) from longest to shortest wavelength.

White light is a mixture of all visible wavelengths. When white light passes through a prism, each wavelength bends by a slightly different amount, separating the light into the familiar rainbow of colors. This process is called dispersion. Violet bends the most and red bends the least, which is why violet appears at the bottom of a prism's rainbow and red at the top.

Photons and Wave-Particle Duality

Light doesn't fit neatly into one category. Sometimes it behaves like a wave (it diffracts, interferes, and has wavelength). Other times it behaves like a stream of particles. This is called wave-particle duality.

The "particle" of light is called a photon, a discrete packet of electromagnetic energy. The energy of a single photon is calculated with:

$E = hf$

• $E$ = energy of the photon (in joules)
• $h$ = Planck's constant ($6.63 \times 10^{-34}$ J·s)
• $f$ = frequency of the light (in Hz)

Higher-frequency light means higher-energy photons. A photon of violet light ($f \approx 7.5 \times 10^{14}$ Hz) carries roughly twice the energy of a photon of red light ($f \approx 4.3 \times 10^{14}$ Hz).

The photoelectric effect is a key piece of evidence for the particle nature of light. When light shines on certain metals, it knocks electrons loose from the surface. The critical finding: only light above a certain frequency (called the threshold frequency) ejects electrons, regardless of brightness. Cranking up the brightness of a dim red light won't eject a single electron, but even faint ultraviolet light will. This only makes sense if light arrives in discrete energy packets rather than as a continuous wave. Each photon either has enough energy to knock an electron free, or it doesn't.

Light Polarization and Applications

Most light sources (the sun, a light bulb) produce unpolarized light, meaning the electric field oscillates in all directions perpendicular to the direction of travel. Polarized light oscillates in just one plane.

A polarizing filter works by blocking all oscillation directions except one. Think of it like a picket fence: only waves aligned with the slats pass through. If you stack two polarizing filters and rotate one 90° relative to the other, no light gets through at all, because the second filter blocks everything the first one let pass.

Practical applications of polarization:

• Polarized sunglasses block horizontally polarized light, which is the main component of glare reflecting off roads, water, and snow. Light reflecting off horizontal surfaces tends to become horizontally polarized, so a vertical filter cuts the glare while still letting other light through.
• LCD screens use two polarizing filters with a liquid crystal layer between them to control which light passes through each pixel.
• Stress analysis in engineering uses polarized light passed through transparent materials. Areas of stress in the material show up as colorful patterns, revealing where deformation is occurring.