Light Fundamentals — Abridged Guide

Quick-reference equations, tables, and rules of thumb for the nature of light, electromagnetic waves, and photon physics. For full derivations, worked examples, and diagrams, see the Comprehensive Guide.

1.Introduction

Light is the working medium of photonics. Three models — ray, wave, and photon — describe its behavior. Each is valid within a specific regime; choosing the simplest adequate model is an engineering skill.

For most catalog component selection, ray optics suffices. Switch to wave optics when features approach the wavelength. Consider photon effects only at low signal levels or when calculating detector limits.

2.Electromagnetic Waves

Speed of Light from Constants

c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} = 299\,792\,458 \;\text{m/s}

Wave Relation

c = \lambda f

Light is a transverse electromagnetic wave. E and B oscillate perpendicular to each other and to the propagation direction. The propagation speed in vacuum is determined entirely by ε₀ and μ₀.

Quick conversion: wavelength (nm) × frequency (THz) ≈ 299 792. For back-of-the-envelope: λf ≈ 3 × 10⁸ m/s.

3.The Electromagnetic Spectrum

Region	Wavelength	Photon Energy	Key Laser Lines
UV	200–400 nm	3.1–6.2 eV	193 nm (ArF), 266/355 nm (Nd:YAG)
Visible	380–750 nm	1.65–3.26 eV	532 nm, 632.8 nm (HeNe)
Near-IR	750 nm – 1.4 μm	0.89–1.65 eV	780–980 nm (diode), 1064 nm (Nd:YAG)
SWIR	1.4–3 μm	0.41–0.89 eV	1310/1550 nm (telecom)
MWIR–LWIR	3–15 μm	0.08–0.41 eV	10.6 μm (CO₂)

The “optical spectrum” in photonics spans ~10 nm to ~1 mm — far beyond visible light. Boundaries between regions are conventions, not physics.

Memorize hc ≈ 1240 eV·nm. Photon energy (eV) = 1240 / wavelength (nm).

4.Energy, Momentum & Intensity

Photon Energy

E = hf = \frac{hc}{\lambda}

Irradiance (Time-Averaged Intensity)

I = \frac{1}{2}\varepsilon_0 c E_0^2

Peak Irradiance — Gaussian Beam

I_{\text{peak}} = \frac{2P}{\pi w^2}

P = power, w = 1/e² beam radius.

A 5 mW HeNe laser emits ~1.6 × 10¹⁶ photons/s. Quantum effects are negligible at typical lab power levels.

Radiation pressure = I/c (absorbing) or 2I/c (reflecting). Sunlight on mirror: ~9 μPa. Negligible for bench optics, relevant for spacecraft.

5.Wave-Particle Duality

Photoelectric Equation

K_{\max} = hf - \phi

K_max = max kinetic energy of ejected electron, ϕ = work function.

Light behaves as a wave (diffraction, interference, polarization) and as particles (photoelectric effect, Compton scattering). The wave model is the default; photon effects matter at low signal levels or energy thresholds.

Experiment	Year	Result	Model Supported
Young's double slit	1801	Interference fringes	Wave
Photoelectric effect	1905	Energy ∝ frequency	Particle
Compton scattering	1923	Photon momentum transfer	Particle
Single-photon interference	Modern	Particle detection, wave pattern	Both

6.Speed of Light

Refractive Index

n = \frac{c}{v}

Group Velocity

v_g = \frac{c}{n - \lambda\,\frac{dn}{d\lambda}}

Pulses travel at v_g. In normal dispersion, v_g < v_p.

c is exact by definition (299 792 458 m/s). In materials, phase velocity = c/n. Pulses travel at group velocity v_g = c/n_g.

Light travels ~30 cm/ns and ~0.3 μm/fs. Useful benchmarks for timing and pulse length.

7.Polarization Fundamentals

Linear, circular, and elliptical are the three polarization states. Thermal/LED sources are typically unpolarized; lasers are often linearly polarized.

Always check polarization when using beam splitters, Brewster windows, or dichroic mirrors. Polarization mismatch is a top cause of unexpected signal loss.

8.Coherence

Coherence Length

L_c = \frac{c}{\Delta\nu}

Source	Linewidth Δν	Coherence Length L_c
Incandescent	~300 THz	~1 μm
LED	~10–30 THz	~10–30 μm
Na lamp	~510 GHz	~0.6 mm
Multimode HeNe	~1.5 GHz	~20 cm
Single-mode HeNe	<500 kHz	>500 m
DFB laser	~1 MHz	~300 m
Fiber laser (SF)	~1–10 kHz	30–300 km

Coherence length determines the maximum path difference for interference fringes. Range: ~1 μm (thermal) to >100 km (fiber lasers).

For interferometry, source L_c must exceed system path difference. For OCT, short L_c (~10 μm) provides depth resolution.

9.Light-Matter Interaction

Beer-Lambert Law

I = I_0\,e^{-\alpha z}

α = absorption coefficient, z = path length.

Snell's Law

n_1\sin\theta_1 = n_2\sin\theta_2

Process	Mechanism	Key Equation	Application
Absorption	Energy transfer to medium	I = I₀e^(−αz)	Spectroscopy, filtering
Reflection	Boundary mismatch	R = [(n₁−n₂)/(n₁+n₂)]²	Mirrors, beam splitters
Refraction	Speed change	n₁ sin θ₁ = n₂ sin θ₂	Lenses, prisms, fiber
Rayleigh scattering	Dipole re-radiation	I ∝ λ⁻⁴	Blue sky, attenuation
Stimulated emission	Photon-triggered decay	Gain coefficient	Lasers

Every optical component exploits absorption, reflection, refraction, scattering, or emission. Material selection depends on which dominates at the operating wavelength.

Normal-incidence reflectance ≈ [(n−1)/(n+1)]². For glass (n=1.5): ~4% per surface. 10 uncoated surfaces → ~34% total loss.

10.Selecting the Right Model

Scenario	Model	Why
Lens system design	Ray	Elements ≫ λ
Mirror alignment	Ray	Geometric tracing
AR coating design	Wave	Film ~ λ/4
Grating spectrometer	Wave	Groove ~ λ
Gaussian beam focusing	Wave	Diffraction limit
Interferometer fringes	Wave	Phase central
Low-light detector SNR	Quantum	Shot noise ∝ √N
Laser gain medium	Quantum	Einstein coefficients
Quantum key distribution	Quantum	Single photon states

Ray optics when d ≫ λ. Wave optics when d ~ λ. Quantum when photon counts are low or energy thresholds matter.

Fresnel number N_F = a²/(λL). If N_F ≫ 1, ray optics is safe. If N_F ≤ 1, wave optics required.

Continue Learning

Comprehensive Light Fundamentals Guide →Coherence Length Calculator →Spectral Unit Converter →Units & Conversions (Abridged) →

The Comprehensive Guide includes 7 worked examples, 7 SVG diagrams, detailed derivations, and 8 cited references covering all topics on this page.