Topic Cluster

Waves & Optics

Waves and optics: oscillations, sound and light as waves — wave speed, frequency and wavelength, interference, reflection and refraction, and how waves carry energy.

Waves and Optics — the core equations of waves and optics, and every article on the topic
The equations this topic keeps coming back to.

What Are Waves and Optics?

Waves and Optics are oscillations that travel: sound and light, and what happens when a wave meets a boundary, a slit or a lens. The same mathematics describes a guitar string and a radio mast.

Core equations in waves and optics
RelationshipEquationWhat it tells you
Wave speedv = f·λSpeed from frequency and wavelength
PeriodT = 1 / fTime for one full oscillation
Refractive indexn = c / vHow much a medium slows light
Snell's lawn1·sinθ1 = n2·sinθ2Refraction at a boundary
Thin lens equation1/f = 1/do + 1/diObject and image distance for a lens
Malus's lawI = I0 · cos²θIntensity through a polarizer
Resonance in Physics
Waves & Optics

Resonance in Physics

Resonance is the large response a system gives when it is driven at or near its own natural frequency, which for a mass on a spring is f0 = (1/2pi) sqrt(k/m) and depends on the stiffness and the mass alone. The half most explanations leave out is how big that response gets: at the natural frequency the amplitude is Q times the deflection the same force would produce held steady, and Q = 1/(2 zeta) is set by the damping and by nothing else. This page proves that with one oscillator, shows why the peak of the response sits slightly below the natural frequency and disappears altogether past a damping ratio of 0.7071, corrects the Tacoma Narrows story, and works eight problems step by step - including the 2.00 N push that turns a 10.00 mm static deflection into a 100.0 mm swing.

21 min read
Interference of Waves
Waves & Optics

Interference of Waves

The interference of waves is what two overlapping waves do to each other: at every point their displacements add, and the only thing that decides the result is how far out of step the two are. One whole wavelength of extra path is one whole cycle of phase, so a path difference of three wavelengths behaves exactly like none at all. This page sets out the two conditions in full, the resultant amplitude and the band it can never leave, why destructive interference moves energy instead of destroying it, what beats are, where the model breaks down, and seven problems worked step by step.

19 min read
Standing Waves and Harmonics
Waves & Optics

Standing Waves and Harmonics

Standing waves are the fixed patterns a wave settles into between two ends, where only the wavelengths that fit a whole number of half waves survive. That one condition, L = n lam / 2, is why a 0.800 m string along which waves run at 400 m/s sounds 250.000 Hz and then 500.000, 750.000 and 1000.00 Hz, and nothing in between. This page sets out where the nodes and antinodes sit, why a 0.500 m pipe stopped at one end drops from 343.000 Hz to 171.500 Hz and loses its even harmonics, why changing the medium moves every frequency without touching the shape, where the model breaks down, and seven problems worked in full.

20 min read
Infrared Radiation: Uses & Properties
Waves & Optics

Infrared Radiation: Uses & Properties

Infrared radiation is the 700 nm to 1 mm slice of the electromagnetic spectrum, just beyond the red end of what the eye can see, and one band name stretched over a factor of 1428.57 in wavelength. This page gives the range and the one relation that governs it, the five published ways of subdividing the band and why they disagree, what sits in each part from remote controls to far-infrared astronomy, why an infrared photon is weak compared with room temperature, and where the simple picture breaks down. Seven worked problems, two original diagrams, an interactive lab and a calculator.

21 min read
Ultraviolet Radiation: Types & Effects
Waves & Optics

Ultraviolet Radiation: Types & Effects

Ultraviolet radiation is the 100 to 400 nm region of the electromagnetic spectrum, split by convention into UVA, UVB and UVC. This page gives the three band boundaries and where they come from, the energy every ultraviolet photon carries in eV, joules and kJ/mol, which bands the atmosphere lets through and why, and the work-function threshold that explains why ultraviolet damages what visible light leaves alone. Seven worked problems, two original diagrams, an interactive lab and a calculator.

19 min read