Light Study Guide

📖 Core Concepts Light – electromagnetic radiation that can produce a visual sensation (human eye). Visible spectrum – wavelengths ≈ 400 nm – 700 nm (frequencies ≈ 750 THz – 420 THz). Speed of light in vacuum – exact constant \(c = 299\,792\,458\ \text{m s}^{-1}\); defines the metre. Electromagnetic spectrum – ordered by wavelength: radio → microwave → infrared → visible → ultraviolet → X‑ray → γ‑ray. Refraction & Snell’s law – light changes direction when \(n{1}\sin\theta{1}=n{2}\sin\theta{2}\); frequency stays constant, wavelength changes. Radiometry vs. Photometry – radiometry = total radiant power (all λ); photometry = power weighted by human eye sensitivity (lumens). Light pressure – photons transfer momentum; pressure \(= \dfrac{P}{c}\) where \(P\) is optical power. Black‑body radiation – any hot object emits a continuous spectrum; peak wavelength shifts with temperature (Wien’s law). Atomic emission & stimulated emission – discrete lines from electron transitions; stimulated emission gives coherent laser light. Historical models – Young/Fresnel (wave), Maxwell (electromagnetic), Planck/Einstein (photon/quantum). 📌 Must Remember Visible λ range: 400 nm – 700 nm. Exact speed of light: \(c = 299\,792\,458\ \text{m s}^{-1}\). Snell’s law: \(n{1}\sin\theta{1}=n{2}\sin\theta{2}\). Light‑pressure formula: \( \displaystyle \frac{P}{c}\) (pressure = power ÷ c). Photopic peak sensitivity: 555 nm (human eye). Black‑body colour progression: red (cool) → white → blue‑white (hot). Cherenkov condition: particle speed \(> c{\text{medium}}\) → visible blue glow. Radiometry unit: watt (W); Photometry unit: lumen (lm). Fermat’s principle: light follows the path of least time. 🔄 Key Processes Refraction at an interface Determine indices \(n{1}, n{2}\). Keep frequency constant → compute new wavelength \(\lambda{2}= \lambda{1}\frac{n{1}}{n{2}}\). Apply Snell’s law to find \(\theta{2}\). Black‑body spectrum shift (Wien’s law) \(\lambda{\text{max}}T = 2.898 \times 10^{-3}\ \text{m·K}\). Increase \(T\) → \(\lambda{\text{max}}\) moves to shorter λ (higher energy). Photon momentum transfer Photon momentum \(p = \dfrac{h}{\lambda}\). For a beam of power \(P\), pressure \(= \dfrac{P}{c}\) (perfect absorption) or \(= \dfrac{2P}{c}\) (perfect reflection). Stimulated emission (laser action) Incident photon of energy \(E = h\nu\) induces excited atom to emit a coherent photon (same phase, direction, wavelength). 🔍 Key Comparisons Radiometry vs. Photometry Radiometry: measures all electromagnetic power (W). Photometry: measures perceived brightness (lm), weighted by V(λ). Absorption (fluorescence) vs. Emission (phosphorescence) Fluorescence: immediate re‑emission, short lifetime (< ns). Phosphorescence: delayed re‑emission, long lifetime (ms‑min). Reflection vs. Refraction Reflection: angle of incidence = angle of reflection; wavelength unchanged. Refraction: change in direction + wavelength due to different \(n\). Thermal (black‑body) light vs. Atomic line light Black‑body: continuous spectrum, colour depends on temperature. Atomic line: discrete wavelengths, independent of temperature. ⚠️ Common Misunderstandings “Light speed changes in a medium” – the phase velocity changes (via \(n\)), but the frequency stays the same; only the wavelength shortens. “All photons have the same energy” – photon energy \(E = h\nu = hc/\lambda\) varies across the spectrum. “Radiometric and photometric readings are interchangeable” – photometric values are weighted by human eye response; a sensor that sees IR will give a radiometric reading, not a photometric one. “Cherenkov radiation means particles exceed \(c\) in vacuum” – it only exceeds light speed in that medium, not the universal constant \(c\). 🧠 Mental Models / Intuition “Light as a fast messenger” – Think of light as a courier that never slows down in vacuum; the medium “adds traffic” (higher \(n\)) that compresses its wavelength but never its speed in vacuum. “Snell’s law as water‑wave refraction” – When a wave enters deeper water (higher \(n\)), it slows and bends toward the normal—exactly what Snell’s law predicts for light. “Black‑body colour ladder” – Imagine heating a metal rod: red → orange → white → blue. The ladder maps temperature → peak λ. 🚩 Exceptions & Edge Cases Total internal reflection – occurs when light tries to go from higher‑\(n\) to lower‑\(n\) at angles > critical angle \(\thetac = \arcsin(n2/n1)\). Anomalous dispersion – near absorption lines, refractive index can decrease with increasing wavelength, violating the usual trend. Polarization dependence – Fresnel’s equations show that s‑ and p‑polarized light reflect/refract differently at oblique incidence. 📍 When to Use Which Snell’s law – use for any interface where ray optics applies (λ ≪ object size). Fermat’s principle – handy for deriving path‑length problems (e.g., lens design, mirror geometry). Radiometric vs. photometric calculations – use radiometry for energy balance, sensor calibration; use photometry for lighting design, human‑vision tasks. Black‑body formulas – apply when dealing with thermal emitters (stars, incandescent lamps). Stimulated emission model – use for laser design, maser, optical amplifiers. 👀 Patterns to Recognize Wavelength ↔ Energy inverse relationship – shorter λ → higher photon energy; useful for identifying UV‑induced chemical effects vs. IR heating. Spectrum location clues – If a source is described as “cool” (≈300 K) → emission peaks in infrared; “hot” (≈6000 K) → peaks in visible. Frequency stays constant across media – whenever a problem mentions a change of medium, keep ν the same, adjust λ via \( \lambda = \dfrac{c}{n\nu}\). Photon‑pressure magnitude – pressure is tiny unless power is huge (e.g., solar sail); look for “large‑area, low‑mass” contexts. 🗂️ Exam Traps Choosing “c” vs. “v” in Snell’s law – some students mistakenly insert \(c\) (vacuum speed) instead of refractive index; remember the law uses \(n\), not speeds. Confusing radiometric watt with photometric lumen – a lamp that emits mostly IR may have high watts but low lumens; answer choices that ignore eye weighting are wrong for lighting questions. Assuming Cherenkov light appears in water at any speed – only particles > \(c{\text{water}} \approx 0.75c\) produce it; lower speeds give none. Misreading “visible light” as any EM radiation – exam items about “light” may refer to the full EM spectrum; check wavelength limits given. Total internal reflection vs. refraction – if incident angle exceeds critical angle, the correct answer is reflection, not refraction. --- Keep this sheet handy – the bullets are designed for rapid recall right before the exam.