Electromagnetic Spectrum

The full spectrum

Visible spectrum

JavaScript — spectrum calculations

const c = 3e8;
const h = 6.626e-34;
const eV = 1.602e-19;

// Convert between f, λ, energy
function freqToWavelength(f) { return c / f; }
function wavelengthToFreq(lam) { return c / lam; }
function freqToEnergy(f) { return h * f; }  // J
function freqToEnergy_eV(f) { return h * f / eV; }
function wavelengthToEnergy_eV(lam) { return h * c / lam / eV; }

// Common parts of spectrum
console.log(`Red light (700 nm): ${wavelengthToEnergy_eV(700e-9).toFixed(2)} eV`);
console.log(`UV (200 nm): ${wavelengthToEnergy_eV(200e-9).toFixed(2)} eV`);
console.log(`X-ray (0.1 nm = 1Å): ${wavelengthToEnergy_eV(0.1e-9).toFixed(0)} eV`);
console.log(`Gamma (10 pm): ${wavelengthToEnergy_eV(10e-12).toFixed(0)} eV`);

// Check ionization energy
const ionization_H = 13.6;  // eV
function canIonize(photon_eV, target_eV = ionization_H) {
  return photon_eV >= target_eV;
}

console.log(`UV (10 eV) ionizes H? ${canIonize(10)}`);  // false
console.log(`UV (15 eV) ionizes H? ${canIonize(15)}`);  // true (UV-C)
console.log(`X-ray (1000 eV) ionizes H? ${canIonize(1000)}`); // yes

// Atmosphere transmission windows
function inVisibleWindow(wavelength) {
  return wavelength >= 380e-9 && wavelength <= 750e-9;
}

function inRadioWindow(frequency) {
  // Atmosphere transparent ~3 MHz to ~30 GHz
  return frequency >= 3e6 && frequency <= 30e9;
}

// Microwave oven: water absorption peak
console.log(`2.45 GHz (microwave) wavelength: ${(c / 2.45e9 * 1000).toFixed(1)} cm`);

// Fiber optic communication uses 1550 nm (low water absorption in glass)
console.log(`Fiber optic 1550 nm: ${(wavelengthToEnergy_eV(1550e-9)).toFixed(2)} eV`);

// 5G radio
function radio5G(freq_GHz) {
  return c / (freq_GHz * 1e9) * 100;  // wavelength in cm
}

console.log(`5G at 28 GHz: ${radio5G(28).toFixed(2)} cm`);  // 1.07 cm

Where each part of spectrum is used

Common mistakes

• Treating visible as "the spectrum." Visible is just one tiny piece. Most EM waves invisible to humans.
• Confusing wavelength and frequency. Inversely related: λ = c/f. Higher frequency = shorter wavelength.
• Mixing energy units. Photon energy can be expressed in J, eV, keV, MeV. Be consistent.
• Forgetting all EM travels at c. Different parts of spectrum have same speed in vacuum (c). Different in matter (different n for different wavelengths — dispersion).
• Treating UV as visible. Just below visible. Bees can see some UV; humans usually can't.
• Fearing all radiation equally. Low-energy photons (radio, microwave, IR) typically not harmful. Ionizing radiation (UV high-energy, X-ray, gamma) requires shielding.