Phy 213 chp 33 copy

Chapter 33: Electromagnetism

Maxwell's Contribution to Electromagnetism

• James Clerk Maxwell's groundbreaking work demonstrated that light is an electromagnetic wave, a traveling wave of electric (E) and magnetic (B) fields.

• This finding establishes optics, the study of visible light, as a subfield of electromagnetism.

Electromagnetic Spectrum Overview

• Frequency and Wavelength Variations

  • The electromagnetic spectrum varies with frequency and wavelength.

  • Key points on the spectrum include:

    • Gamma rays

    • X-rays

    • Ultraviolet (UV)

    • Infrared (IR)

    • Microwaves

    • Radio waves

  • Visible light is centered around 555 nm in wavelength.

Properties of Electromagnetic Waves

• Wave Characteristics:

  1. The electric field (E) and magnetic field (B) are always perpendicular to each other and the direction of wave propagation, which confirms they are transverse waves.

  2. E and B fields vary sinusoidally and are in phase with one another.

• Electromagnetic Wave Equation:

  • An electromagnetic wave traveling along the x-axis has electric field E and magnetic field B magnitudes that change with position (x) and time (t).

  • The parameters include:

    • Em: amplitude of electric field E

    • Bm: amplitude of magnetic field B

    • w: angular frequency

    • k: angular wave number

Poynting Vector and Energy Transport

• Poynting Vector denotes the rate at which energy is transported through an electromagnetic wave.

  • Energy density of electric field (uE) equals energy density of magnetic field (uB).

  • The time-averaged intensity (I) is calculated using:

    • I = Savg

  • Intensity relates to energy associated with electric and magnetic fields.

Intensity Variation and Sources

• A point source emits electromagnetic waves isotropically.

• Intensity (I) at distance r from power source P:

  • I = P/(4πr²) shall be used to determine the intensity variation with distance.

Polarization of Light Waves

• Definition of Polarization:

  • Light waves are polarized when their electric field vectors align in a single plane, termed the plane of oscillation.

  • Common light sources emit unpolarized or randomly polarized light.

• Transmission Through Polarizing Sheets:

  • For unpolarized light through a polarizer, transmitted intensity is half: I = 0.5 I₀.

  • If the light is polarized, the transmitted intensity is dependent on the angle θ between the original light's polarization direction and the polarizing sheet direction, using the formula:

    • I = I₀ cos²(θ)

Refraction and Reflection

• Ray of Light Mechanics:

  • A ray travels through various media. When it meets a boundary, part of it reflects back into the original medium and some refracts.

  • The angle of reflection equals the angle of incidence.

• Refraction Summary:

  • Governed by Snell’s Law: n = c/v, where n is the refractive index.

  • Refraction effects include:

    1. If n₂ = n₁, θ₂ = θ₁ (no bending)

    2. If n₂ > n₁, θ₂ < θ₁ (bends toward the normal)

    3. If n₂ < n₁, θ₂ > θ₁ (bends away from the normal)

Total Internal Reflection

• Occurs when light moves from a medium with a higher refractive index to a lower one and exceeds the critical angle.

• Critical angle: θc, where sin(θc) = n₁/n₂ allowing for the possibility of total internal reflection.

Chromatic Dispersion

• White light disperses into its components upon refraction through materials, causing different wavelengths (e.g., blue light) to refraction at varying angles, leading to phenomena like rainbows.

Brewster Angle and Polarization by Reflection

• At Brewster's angle (θB), incident light reflecting off surfaces becomes polarized.

• Reflected light consists of electric field components perpendicular to the plane of incidence, while refracted light contains both parallel and perpendicular components.

Problem Solving with Electromagnetic Waves

• Example of intensity calculation from a transmitter:

  • Given intensity at a point, relate it to the electric field amplitude using formulas involving intensity and the amplitude of the electric field.

• For multi-sheet polarization systems, demonstrate the conditions necessary to achieve a desired intensity after passing through polarizing sheets, requiring calculations based on cosines.