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Wien’s Displacement Law — formula and the two peak wavelengths to know?
essential emr

Hot things glow short, cool things glow long. That’s the whole law in plain terms.

  • The Sun is super hot, so it glows in visible light (we can see it).
  • The Earth is cool, so it glows in thermal infrared (we can’t see it, but our sensors can).

That’s exactly why we use VIS/NIR sensors to capture reflected sunlight, and thermal infrared sensors to capture Earth’s own heat — at night, in the dark, all the time.

🔬 Science / formula

λ_max = 2897.8 / T (µm, T in K)

  • Sun (~6000 K): λ_max ≈ 0.483 µm (visible)
  • Earth (~300 K): λ_max ≈ 9.66 µm (thermal IR)

Hotter → shorter peak wavelength.

💡

Hot = short, cool = long. Sun hot → 0.48 µm (visible). Earth cool → 9.66 µm (thermal IR). That's why we use VIS/NIR for reflected solar and thermal IR for emitted Earth.

emr/wien-law ✎ edit content

Stefan–Boltzmann Law?
essential emr

How brightly something glows depends on its temperature to the fourth power — meaning a small temp jump produces a huge brightness jump.

  • Double the temperature → 16× the radiation.
  • Triple it → 81×.

That’s why a campfire feels exponentially warmer than warm tea, and why thermal satellite sensors can detect 1°C differences across a landscape — the signal isn’t subtle once you know to look at the right wavelength.

🔬 Science / formula

M_λ = σ · T⁴ — total emitted power per m² from a blackbody.

  • σ = 5.6697 × 10⁻⁸ W/(m²·K⁴)
  • T in Kelvin
  • Real objects: ε · σ · T⁴ (ε = emissivity)
  • Emitted energy scales with T⁴ — why thermal sensors are so sensitive.
💡

SB = Super Boost. T to the FOURTH — double the temp, 16× the energy. That's why a 300 K Earth emits radiation at all.

emr/stefan-boltzmann ✎ edit content

Three types of atmospheric scattering?
essential emr

Classified by particle size relative to wavelength:

  • 🟦 Rayleigh — particles ≪ λ
    • Source: air molecules (N₂, O₂)
    • Affects: short wavelengths most (1/λ⁴ dependence)
    • Result: blue sky at noon, red at sunset
  • 🌫️ Mie — particles ≈ λ
    • Source: dust, smoke, aerosols, pollen
    • Affects: longer wavelengths and all of visible
    • Result: hazy skies
  • ☁️ Non-selective — particles ≫ λ
    • Source: water droplets, ice crystals
    • Affects: all wavelengths equally
    • Result: white clouds (B + G + R scattered equally → white)
💡

Rayleigh → blue sky (short wins). Mie → haze (particles match wavelength). Non-selective → white clouds (big droplets scatter ALL colors equally = white).

emr/scattering-three-types ✎ edit content

Active vs passive remote sensing?
likely emr
  • 👂 Passive — sensor only receives natural energy
    • Source: solar reflection or target’s thermal emission
    • Examples: Landsat, MODIS, SPOT, IKONOS
    • Limit: needs the Sun (or warm objects for thermal)
  • 📢 Active — sensor emits its own pulse and measures the return
    • Works day or night, often through clouds
    • Examples: Radar, LiDAR, scatterometers

Mnemonic: passive listens; active shouts and listens.

💡

Passive = listens. Active = shouts and listens. Active works at night (radar/LiDAR don't need the sun).

emr/active-vs-passive ✎ edit content

Atmospheric windows — which spectral regions transmit well?
likely emr

Bands where the atmosphere lets EM radiation through to the sensor:

  • 🟦🟩🟥 Visible (0.4 – 0.7 µm)
  • 🟪 Near-infrared (0.7 – 1.3 µm)
  • 🟫 Middle / shortwave IR (1.3 – 3.0 µm, with gaps)
  • 🔥 Thermal IR
    • 3.0 – 5.0 µm (smaller window)
    • 8 – 14 µm (big thermal window — Landsat TIRS lives here)
  • 📡 Microwave (1 mm – 1 m) — radar; essentially all-weather

⚠️ Blocked regions are dominated by H₂O and CO₂ absorption.

emr/atmospheric-windows ✎ edit content