Light, vision, and photography

Waves

• An electro-magnetic (EM) wave is a signal carrying energy through space/time, with a physical value at each space-time point given by the strength of its electrical and magnetic fields. These fields oscillate perpendicular to the path of the wave (so EM waves are transverse).
• EM waves travel through a vacuum (no medium)
• EM waves travel at a fixed speed v = approximately 3 x 10^8 (300 million) meters/second, or 186,000 miles/sec.
• Like periodic sound waves, periodic EM waves are characterized by their:
  • Period: T
  • Frequency: f = 1/T
  • Wavelength: L = v*T = v/f, i.e. v = f*L, f=v/L (higher frequency means lower wavelength)
  • Amplitude: A
  • Power: proportional to A^2
• Like sound waves, EM waves can be analyzed as the sum of sine and cosine waves at different frequencies and amplitudes, using the Fourier theorem
• Light comprises a frequency range within the EM spectrum in the visible range: 750 - 390 nanometers (billionths of a meter), i.e. frequencies in the range 400 to 790 terahertz (tera = trillion = 10^12), corresponding to colors ROYGBIV (red-orange-yellow-green-blue-indigo-violet)
  • Waves (transverse, longitudinal)(1D, 2D, 3D).
  • Wave front (0D, 1D, 2D)
  • Inverse square law: in the absence of boundaries, waves spread. In 3D, the spread is proportional to the square of the distance from the source. If the power (energy per unit time) is constant, then intensity (power per unit area) is inversely proportional to the square of the distance. What this means: a flashlight's intensity at 8 feet is only a quarter its intensity at 4 feet.
  • Wave amplitude (A): the amplitude is the difference between the wave's maximum and minimum values.
  • Wave power (P = A^2): waves carry energy; the power (energy per unit time) carried by a wave is proportional to the square of its amplitude.
  • We measure the "difference" in power between two waves using a logarithmic scale, dB, applied to the power ratio between the two waves, which is the square of the amplitude ratio
  • dB = 10*Log(power ratio) = 10*log(A ratio squared) = 20 * log (A)
  • [recall from high school math that log(A squared) = 2 log (A) ]
  • Wave superposition principle: in a linear medium, waves combine simply by adding their values. Traveling waves will appear to pass through each other unscathed. It's also possible to cancel a wave by adding its inversion (as in noise canceling headphones). See this simple 1D string animation, or play with this ripple tank.
  • Reflection: a wave will reflect off a reflective boundary, partially (glass) or fully (mirror).
  • Diffraction: while light shadows appear relatively sharp (compared to sound shadows), a light wave can travel around an obstacle significantly smaller than its wavelength (see periodic waves, below), and will spread after passing through a hole.
  • Refraction: a wave changes direction when the medium changes.
  • Light waves are tranverse traveling electromagnetic waves through space (no medium) in 3D.