Two sources 3 wavelengths apart

At its defaults it draws two sources 3 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.

two-source-interference is one function in lib/figures/waves.js — travelling, standing, adding and shifting. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

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.

A plane wavefront, with 9 points on it treated as sources and a wavelet of radius vt drawn about each. The envelope of those circles — the curve touching all of them — is a second straight line, parallel to the first and displaced by exactly vt. That is the whole of straight-line propagation: nothing else has to be assumed, and in particular nothing has to be said about rays, which are afterwards defined as the normals to these fronts. The construction is drawn with the wavelets left in, because they are the part that does the work.

A plane wavefront, with 5 points on it treated as sources and a wavelet of radius vt drawn about each. The envelope of those circles — the curve touching all of them — is a second straight line, parallel to the first and displaced by exactly vt. That is the whole of straight-line propagation: nothing else has to be assumed, and in particular nothing has to be said about rays, which are afterwards defined as the normals to these fronts. The construction is drawn with the wavelets left in, because they are the part that does the work.

A plane front arriving at 40° at the boundary between media of index 1 and 1.5. Each point of the surface starts a wavelet at the moment the front reaches it, so the wavelet that started first is the largest — and every one of them is smaller than it would have been by the factor 0.667, because that is the ratio of the speeds. The envelope of those unequal circles is a straight front tilted by the angle the delay builds up, and the ray perpendicular to it leaves at 25.37° to the normal. The drawn front touches all 9 drawn wavelets to within 2.8e-14 of a pixel, which is the figure's own check on itself: the bend is a consequence of the delay and of nothing else, and a slower medium is one in which the far side of a front gets ahead.

The same construction through apertures of 0.8, 2, 6 wavelengths. In the middle of a wide aperture the wavelets still have neighbours on both sides and their envelope is straight; at the edges they do not, and the envelope curls round into the geometric shadow. The angle to the first direction in which the wavelets cancel is arcsin(λ/w) — 90.0°, 30.0°, 9.6° — so an aperture one wavelength wide spreads into the whole half-space and one six wavelengths wide barely spreads at all. Ray optics is what this construction becomes when the aperture is enormous compared with the wavelength, which is why it took a thousand years to notice it was wrong.

The same construction through apertures of 1, 3, 12 wavelengths. In the middle of a wide aperture the wavelets still have neighbours on both sides and their envelope is straight; at the edges they do not, and the envelope curls round into the geometric shadow. The angle to the first direction in which the wavelets cancel is arcsin(λ/w) — 90.0°, 19.5°, 4.8° — so an aperture one wavelength wide spreads into the whole half-space and one six wavelengths wide barely spreads at all. Ray optics is what this construction becomes when the aperture is enormous compared with the wavelength, which is why it took a thousand years to notice it was wrong.

physicscheck asserts something about two-source-interference that could fail — it draws it and measures the result against a value reached some other way.

Across the library: 100 interrogated, 2 exercised only, 1 untouched, of 103. Read out of the gate's source by the gate's own two patterns — and the gate's last claim fails the build if that read disagrees with what it was handed while running.