Illustrated Physics
physics, drawn
Concept

Airy pattern — where it appears

The pattern of light diffracted by a circular aperture or disc: a bright central spot ringed by fainter rings. Its first dark ring lies at an angle whose sine is 1.22 wavelengths over the diameter, which sets a telescope's resolution and the size of a corona round the Moon.

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 Every colour makes the same rings at its own size. The light diffracted forward by water drops 15 µm across, as a fraction of its brightness at the Moon's centre, on a logarithmic scale, for blue, green and red light. Each is Airy's pattern for an opaque disc the size of the drop: a bright central disc, the aureole, then rings. The rings scale with wavelength, so blue's first dark ring falls at 2.1° and red's at 3.0°. Where blue has gone dark red is still bright, which is why the aureole's edge is reddish brown and each later ring is blue inside and red outside.

The ring round the Moon that sizes a droplet

On a night of thin cloud the Moon sometimes sits in a small disc of pale light edged with brown, with faint coloured rings outside it. That corona is not refraction, which makes the much larger halo, but diffraction by the cloud's droplets, each acting as a tiny opaque disc. The size of the rings is a measurement of the size of the drops, the number of rings is a measurement of how alike they are, and an oval corona says the particles are not drops at all.

optics · Diffraction

Named alongside it

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

Angular resolutionApertureBabinets principleCloud dropletsDe broglie wavelengthDiffractionDiffraction limitLunar coronaNumerical aperturePoint-spread functionPolydispersityRayleigh's criterion

All concepts