Illustrated Physics
physics, drawn
Concept

Angular resolution — where it appears

The smallest angle between two sources an instrument can report as two, fixed by the wavelength over the aperture width rather than by the optics. Improving it means a larger aperture or a shorter wavelength, and no amount of magnification or polishing substitutes for either.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The dip that decides it. Two equally bright points seen through a circular aperture, their Airy patterns added, at 0.7, 1, 1.6 times the Rayleigh separation. Below each is the depth of the dip between the peaks, measured off the drawn sum: 0.0%, 26.5%, 91.6%. At exactly the Rayleigh separation the dip is 26.5% — the criterion is a convention about how much of a dip a detector can see, not a threshold anything crosses. Below it the two peaks merge into one and the pair is gone; above it the answer was never in doubt.

How far apart two things have to be

An instrument's ability to tell two things apart is not set by the quality of its glass. It is set by the width of the hole light comes through, by a factor that is the first zero of a Bessel function — and the threshold everyone quotes is a convention laid over a computed dip of 26.5 per cent.

optics · Diffraction Two sources 4 wavelengths apart. Circular wavefronts from two sources, with the lines along which they arrive in step drawn through the pattern. Those lines are where the path difference is a whole number of wavelengths.

Why two lamps never interfere

Adding amplitudes is unconditional; fringes are not. What decides is whether the phase difference holds still for longer than a detector takes to record it — and a 10 nm slice of white light holds it for 100 femtoseconds, across a path of 30 micrometres.

optics · Coherence

Named alongside it

The objects these essays reach for when they reach for this one.

Airy patternApertureBandwidthBeatsCoherenceDe broglie wavelengthDiffraction limitInterferenceNumerical aperturePath differencePoint-spread functionRayleigh's criterion

All concepts