15.2 The Behavior of Electromagnetic Radiation

Electromagnetic radiation behaves differently in various media, changing speed and direction. It follows specific laws like Snell's law for refraction and can undergo total internal reflection. The wave equation links frequency, wavelength, and speed, allowing us to calculate these properties.

Light polarization affects how waves oscillate, and interference can create bright or dark fringes. The electromagnetic spectrum covers all types of radiation, from radio waves to gamma rays. Understanding these properties helps explain phenomena like dispersion in prisms.

Properties and Behavior of Electromagnetic Radiation

Behavior of electromagnetic radiation

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• Electromagnetic radiation travels at different speeds in various media
  • In a vacuum, it propagates at the speed of light ($c \approx 3 \times 10^8 \text{ m/s}$)
  • In other media (glass, water), the speed is slower than $c$
    • Speed in a medium calculated by $v = \frac{c}{n}$, where $n$ represents the refractive index of the medium
• When electromagnetic radiation passes from one medium to another, it may change direction due to refraction
  • Angle of refraction depends on refractive indices of media and angle of incidence
    • Snell's law describes relationship: $n_1 \sin \theta_1 = n_2 \sin \theta_2$, where $n_1$ and $n_2$ are refractive indices, and $\theta_1$ and $\theta_2$ are angles of incidence and refraction
• Total internal reflection occurs when angle of incidence exceeds critical angle as light travels from higher to lower refractive index medium
  • Critical angle calculated by $\theta_c = \arcsin(\frac{n_2}{n_1})$, where $n_1 > n_2$
• Diffraction occurs when electromagnetic waves encounter obstacles or openings, causing the waves to bend around edges or spread out

Wave equation calculations

• Wave equation relates frequency ($f$), wavelength ($\lambda$), and speed ($v$) of electromagnetic waves: $v = f\lambda$
  • Frequency: number of wave cycles per second, measured in hertz (Hz)
  • Wavelength: distance between consecutive wave crests or troughs, usually measured in meters (m)
  • Speed: rate at which wave propagates through medium, measured in meters per second (m/s)
• Given any two quantities, the third can be calculated using wave equation
  • Example: if frequency and wavelength known, speed found using $v = f\lambda$
• In a vacuum, speed of electromagnetic waves always equal to speed of light ($c$)
  • Wave equation becomes $c = f\lambda$
• Amplitude of an electromagnetic wave represents the maximum displacement from equilibrium position

Light polarization and interference

• Polarization: orientation of electric field oscillations in electromagnetic wave
  • Light can be linearly polarized (single plane), circularly polarized (rotating), or unpolarized (random directions)
• Polarizing filters control light polarization
  • When light passes through polarizing filter, only component of electric field parallel to filter's axis transmitted
  • Transmitted light intensity follows Malus's law: $I = I_0 \cos^2 \theta$, where $I_0$ is initial intensity and $\theta$ is angle between polarizer and light's initial polarization
• Thin-film interference occurs when light reflects from top and bottom surfaces of thin film, causing constructive or destructive interference
  • Constructive interference: path difference between two reflected waves is integer multiple of wavelength, resulting in bright fringe
    • Condition for constructive interference: $2nd = m\lambda$, where $n$ is refractive index of film, $d$ is film thickness, $m$ is integer, and $\lambda$ is wavelength of light in film
  • Destructive interference: path difference is half-integer multiple of wavelength, resulting in dark fringe
    • Condition for destructive interference: $2nd = (m + \frac{1}{2})\lambda$

Electromagnetic spectrum and dispersion

• The electromagnetic spectrum encompasses all types of electromagnetic radiation, ranging from radio waves to gamma rays
• Dispersion occurs when different wavelengths of light travel at different speeds through a medium, causing separation of colors (as seen in a prism)