trig 8/20/25

1. The Electromagnetic (EM) Spectrum

  • The EM spectrum encompasses the entire range of electromagnetic radiation, from very short wavelength gamma rays to very long wavelength radio waves.

  • Electromagnetic radiation is a form of energy that behaves both like a wave and like a stream of particles called photons.

2. Properties of EM Waves

  • Wavelength (λ\lambda): The distance between two consecutive crests or troughs of a wave.

    • Measured in meters (m).

    • Shorter wavelength means higher energy.

  • Frequency (ff or ν\nu): The number of waves that pass a fixed point in unit time.

    • Measured in Hertz (Hz), which is equivalent to cycles per second (s−1)(s^{-1}).

    • Higher frequency means higher energy.

  • Speed of Light (cc): All EM waves travel at the speed of light in a vacuum.

    • c≈3.0×108 m/sc \approx 3.0 \times 10^8 \text{ m/s}

  • Relationship between cc , λ\lambda , and ff:

    • c=λfc = \lambda f (Speed of light equals wavelength times frequency)

  • Energy (EE): The energy of a photon is directly proportional to its frequency.

    • E=hfE = h f (where hh is Planck's constant, approximately 6.626×10−34 J⋅s6.626 \times 10^{-34}\text{ J}\cdot\text{s})

    • This also means E=hcλE = \frac{hc}{\lambda}.