Waves & Light: every key term you need (+ practice quiz)

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• Fluids
• Thermodynamics
• Electric Forces & Potential
• Circuits
• Magnetism

Wave Properties

Wavelength λ (distance between peaks), frequency f (cycles per time), period T = 1/f, amplitude A (max displacement).

Wave Speed

v = fλ = λ/T. Depends on medium. Light in vacuum: 3×10⁸ m/s. Sound in air: ~340 m/s.

Transverse vs Longitudinal

Transverse: oscillations perpendicular to wave motion (light, water). Longitudinal: oscillations parallel (sound).

Interference

Constructive: peaks align (amplitude increases). Destructive: peak+trough cancel (amplitude decreases).

Double Slit

Light passes two slits; creates interference pattern. Bright: path difference = nλ. Dark: path difference = (n+1/2)λ.

Diffraction

Wave bends around obstacles/edges. Single slit: dark when sin θ = nλ/w. Limits resolution (can't distinguish close objects).

Doppler Effect

Observed frequency changes if source moving. f' = f(v ± v_observer)/(v ± v_source). Blue-shift: approaching, red-shift: receding.

Standing Waves

Interference of wave and reflection; nodes (no motion), antinodes (max motion). Fundamental + harmonics.

Unit 6 Summary

Waves: v=fλ. Interference: constructive/destructive. Diffraction limits resolution. Doppler: motion changes frequency.

Double-Slit Fringe Spacing

Bright fringes at d sinθ = mλ; on a distant screen y_m ≈ mλL/d. Spacing grows with λ and L, shrinks with d. Red fringes are wider apart than blue; immersing in water shrinks them by 1/n.

Single-Slit Diffraction

Dark fringes at a sinθ = mλ (m ≠ 0). Central maximum is twice as wide as the others and narrows as the slit widens; a slit narrower than λ spreads light nearly uniformly.

Diffraction Grating

Same condition d sinθ = mλ as two slits, but many slits make maxima extremely sharp and bright. Grating spacing d = 1/(lines per meter). Higher orders may not exist if sinθ would exceed 1.

Thin-Film Interference

Reflection off a higher-n medium adds a half-wavelength phase shift; off a lower-n medium, none. Path difference in the film is 2t using λ_film = λ/n_film. Count phase shifts (0 or 1 net) to decide which condition gives constructive.

Soap Film Colors

A vertical soap film thins at the top: where t → 0 the single reflection phase shift gives destructive interference, so the top looks dark. Colors appear where 2nt = (m + ½)λ for particular λ.

Snell's Law and Refraction

n₁ sinθ₁ = n₂ sinθ₂. Light entering a denser medium bends toward the normal, slows (v = c/n) and shortens its wavelength (λ = λ₀/n) but keeps its frequency.

Total Internal Reflection

Only from higher n to lower n; critical angle sinθ_c = n₂/n₁. Above θ_c all light reflects — fiber optics, diamond sparkle. From air into water, TIR is impossible.

Dispersion

n varies with wavelength (larger for blue), so a prism spreads white light with violet bent most. Rainbows form from refraction, internal reflection, and dispersion in droplets.

Thin Lens Equation

1/f = 1/d_o + 1/d_i with m = −d_i/d_o. Real images: d_i > 0, inverted. Converging lens forms a virtual, upright, enlarged image when the object is inside f (magnifier).

Mirror Sign Conventions

Concave mirrors: f > 0; convex mirrors: f < 0 and always give virtual, upright, reduced images. Radius of curvature R = 2f. Plane mirror: image as far behind as object is in front, m = +1.

Ray Diagram Rules

For lenses: parallel ray → through far focus; through-center ray → undeviated; through near focus → exits parallel. Any two rays locate the image; the third checks it.

Polarization

Only transverse waves polarize. Malus's law: I = I₀cos²θ through a second polarizer; unpolarized light through the first loses half its intensity. Reflection off nonmetals partially polarizes light horizontally.

Doppler for Light and Sound

Approaching source raises received frequency; receding lowers it. For light, redshift indicates recession — the observational basis of the expanding universe. Frequency changes; the speed of the wave in the medium does not.

Beats

Two nearby frequencies f₁ and f₂ produce amplitude pulsing at f_beat = |f₁ − f₂|. Used to tune instruments; the beat frequency drops to zero when they match.

Resonance in Tubes and Strings

String or open-open pipe: f_n = nv/2L (all harmonics). Closed-open pipe: f_n = nv/4L, odd n only, so its fundamental is an octave lower than an open pipe of the same length.

Wave Speed on a String

v = √(T/μ). Quadrupling tension doubles speed and doubles every harmonic frequency; a thicker string (higher μ) sounds lower at the same tension.