Lecture 7:Electromagnetic Waves Notes

Electromagnetic Waves

• Electromagnetic waves are created by leading electric and magnetic fields feeding off one another.

• They travel at the speed of light.

• They are transverse and can be polarized.

• EM waves interact with atoms, exchanging energy in fixed amounts called quanta.

Classical vs. Quantum Understanding

• Electromagnetic waves can be understood classically (oscillating electric and magnetic fields) and quantum mechanically (energy levels).

• These understandings are complementary; the appropriate one depends on the scale.

Creation of Electromagnetic Fields

• Separating positive and negative charges creates an electric field.

• Moving charges (electric current) creates a magnetic field.

• Changing electric fields create magnetic fields, and vice versa.

• It takes time for the field to set up throughout space.

• Flipping the charges creates a field that changes direction and propagates through space.

Electromagnetic Wave Pattern

• Continuous flipping of charges creates a wave pattern of electric fields moving through space.

• These changing electric fields create magnetic fields at right angles to the electric field.

• Using a sine wave for the charge oscillation results in an electromagnetic wave with electric and magnetic fields perpendicular to each other.

Maxwell's Discovery

• James Maxwell discovered that changing fields of one type (e.g., magnetic) create changing fields of the other type (e.g., electric), allowing them to feed on one another and create a wave.

• This means the fields can exist independently, without charges being pushed around.

Wave Description

• Waves can be described mathematically using equations like:

  $y = A \cos(2\pi ft + \phi)$

  Where:

  • $y$ is the displacement of the wave.

  • $A$ is the amplitude (maximum displacement).

  • $f$ is the frequency.

  • $t$ is time.

  • $\phi$ is the phase angle.

• In the case of electromagnetic waves, the displacement is the electric field, and $A$ is the maximum electric field.

Speed of Electromagnetic Waves

• The speed of an electromagnetic wave can be calculated using:

  $v = \frac{1}{\sqrt{\mu<em>0 \epsilon</em>0}}$

  Where:

  • $\mu_0$ is the permeability of free space (related to magnetic fields around current-carrying wires).

  • $\epsilon_0$ is the permittivity of free space (related to electric charges and their separation).

• This equation combines constants from electricity and magnetism to give the speed of light.

Relationship Between Speed, Frequency, and Wavelength

• The speed of a wave is related to its frequency and wavelength by:

  $v = f \lambda$

  Where:

  • $v$ is the speed of the wave.

  • $f$ is the frequency.

  • $\lambda$ is the wavelength.

Electromagnetic Spectrum

• The electromagnetic spectrum includes a wide range of frequencies and wavelengths, including:

  • Visible light (colors).

  • Ultraviolet (beyond violet).

  • Infrared (beyond red).

  • Microwaves.

  • Radio waves (AM, FM).

  • X-rays.

  • Gamma rays.

  • Cosmic rays.

• All these are electromagnetic waves but are perceived differently due to their varying wavelengths.

Wave Behavior and Wavelength

• When a wave encounters an aperture:

  • If the wavelength $(\lambda)$ is much smaller than the width of the aperture $(d)$, the wave passes straight through, and wave properties are not noticeable.

  • If (\lambda) << d, no wave properties are noticed.

  • If the wavelength is comparable to the aperture size, the wave bends (diffracts) into the region that would otherwise be a shadow, and wave nature becomes apparent.

• X-rays (wavelength ~ $10^{-10}$ meters) can produce sharp images of bones because their wavelength is much smaller than the features being imaged.

• Radio waves (wavelength ~ meters to hundreds of meters) bend around objects like trees and signs because their wavelength is comparable to or larger than these objects.

Microwave Oven Example

• Microwave ovens operate at frequencies of 902,560 MHz.

• The smallest wavelength in a microwave oven is about 11 centimeters.

• The holes in the microwave door should be much smaller than the wavelength (around 1 centimeter or smaller) to prevent the waves from leaking out.

Transverse Waves and Polarization

• Electromagnetic waves are transverse waves, meaning the field oscillates perpendicular to the direction of travel.

• The electric field can oscillate in the x or y direction or any combination thereof.

• A polarizer is a device that selects the electric field oscillating in one particular direction.

• If light is coming straight at you, and electric field is oriented randomly, a polarizer will select the field oscillating in one direction. If a diagonal electric field is presented to a vertical polarizer, only the vertical component will get through.

Reflection and Polarization at Surfaces

• When light hits a surface, the electric field wiggles the charges, setting up an electromagnetic wave, which is reflection.

• In insulators, it's harder for the vertical component of the electric field to be reflected than the horizontal component.

• Unpolarized light has both horizontal and vertical components.

• When light hits a surface, the surface predominantly reflects the horizontal component.

Polarized Sunglasses

• Polarized sunglasses reduce glare by taking advantage of the reflection and polarization properties of light.

• They block horizontally polarized light, which is the light that is predominantly reflected off surfaces.

• Glare is light that's coming off of a surface. The light coming off that surface is horizontally polarized because the surface is flat. The polarizer in polarized sunglasses reject that light.

• Vertical light is usually poorly reflected by road surfaces.

Energy of Electromagnetic Waves

• The intensity of an electromagnetic wave (power per unit area) is given by:

  $I = c \epsilon<em>0 E</em>{max}^2$

  Where:

  • $c$ is the speed of light.

  • $\epsilon_0$ is the permittivity of free space.

  • $E_{max}$ is the maximum electric field.

• The intensity is proportional to the maximum electric field squared.

Quantum Understanding of Light

• At the atomic level, electrons in atoms can only occupy specific orbits.

• Movement of an electron between orbits is coupled to the emission or absorption of electromagnetic radiation.

• The amount of energy emitted or absorbed is called a quantum or photon.

• Classical physics could not explain the discrete spectral lines observed in hydrogen.

• Energy of photon emitted is proportional to the frequency of the light.

Quantitative Aspects of Photons

• It takes about 13.6 electron volts (eV) to remove an electron from a hydrogen atom (typical ionization value).

• The wavelength of a photon with this energy is around 90 nanometers.

• Planck's constant multiplied by the speed of light is $hc$, which equals $1240$ electron-volt nanometers.

• Intensity can be thought of as field squared, or as a number of photons.

• $1 \text{ eV} = 1.6 \times 10^{-19} \text{ Joules}$.

• Atoms measure energy in electron volts.

• The wavelength of a 3 eV photon is about $412$ nm, a violet photon.

Microwave Radiation Energy

• The energy of a microwave photon is about $10^{-5}$ eV.

• Although a million microwave photons contain more energy than one UV photon, they cannot substitute for a UV photon in ionizing an atom.

Atomic Absorption and Emission Spectra

• Atoms have very sharp discrete wavelengths.

• Molecules and solids have bands of wavelengths that get absorbed next to each other.

• For example, hemoglobin has places that are really absorbing particularly Violet and green-orange.

• The broad absorption of hemoglobin is not an artifact; it is broad by nature.

Color Vision and Visual Receptors

• The absorption of light by our eyes allows us to see.

• The visual system has two types of receptors: rods and cones.

  • Rods: Have a big absorbance peak around 500 nanometers (blue-green region). All purpose.

  • Cones: Three types - red, green, and blue. The color of your cones.

• Red, green, and blue are the primary colors in the additive color world.

• Cones are located at the point of sharpest vision.

Miscellaneous

• The yellow region is rather small. Decoded by virtue of how much blue, green, and red have been stimulated.

• A composite of red and green make yellow.

• Plants are green because the region where there is very little absorbance is the green region, whereas red, there is absorbance.

Summary of Key Ideas

• Changing electric fields generate magnetic fields, and vice versa.

• Electromagnetic waves travel at the speed of light.

• Electromagnetic waves are transverse and can be polarized.

• At the atomic level, only certain electron orbits are stable, and changes correspond to the emission or absorption of light.

• Color vision is due to three different receptors.