The two reflectances, and the angle one of them loses

At its defaults it draws the two reflectances, and the angle one of them loses. Reflectance against angle of incidence for light going from n = 1 into n = 1.5. The upper curve is light polarised with its electric field along the surface, which reflects more and more strongly until at grazing incidence everything reflects. The lower curve is light polarised in the plane of incidence, and it does something the other cannot: it falls to exactly zero at 56.31°, where tan θ = 1.5000, and then rises again. At normal incidence the two are equal at 4.00% because there is no plane of incidence to tell them apart. The dashed curve is the transmittance, computed from the transmission coefficients and the two media's projected impedances rather than as one minus the reflectance; it agrees with one minus the reflectance to 4.4e-16 across the whole range, which is where the energy accounting can be seen to close.

fresnel-coefficients is one function in lib/figures/optics.js — rays, lenses, mirrors and what light does to a surface. 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.

Reflectance against angle of incidence for light going from n = 1 into n = 1.5. The upper curve is light polarised with its electric field along the surface, which reflects more and more strongly until at grazing incidence everything reflects. The lower curve is light polarised in the plane of incidence, and it does something the other cannot: it falls to exactly zero at 56.31°, where tan θ = 1.5000, and then rises again. At normal incidence the two are equal at 4.00% because there is no plane of incidence to tell them apart. The dashed curve is the transmittance, computed from the transmission coefficients and the two media's projected impedances rather than as one minus the reflectance; it agrees with one minus the reflectance to 4.4e-16 across the whole range, which is where the energy accounting can be seen to close.

Reflectance against angle of incidence for light going from n = 1 into n = 1.5. The upper curve is light polarised with its electric field along the surface, which reflects more and more strongly until at grazing incidence everything reflects. The lower curve is light polarised in the plane of incidence, and it does something the other cannot: it falls to exactly zero at 56.31°, where tan θ = 1.5000, and then rises again. At normal incidence the two are equal at 4.00% because there is no plane of incidence to tell them apart. The dashed curve is the transmittance, computed from the transmission coefficients and the two media's projected impedances rather than as one minus the reflectance; it agrees with one minus the reflectance to 4.4e-16 across the whole range, which is where the energy accounting can be seen to close.

Reflectance against angle of incidence for light going from n = 1 into n = 1.5. The upper curve is light polarised with its electric field along the surface, which reflects more and more strongly until at grazing incidence everything reflects. The lower curve is light polarised in the plane of incidence, and it does something the other cannot: it falls to exactly zero at 56.31°, where tan θ = 1.5000, and then rises again. At normal incidence the two are equal at 4.00% because there is no plane of incidence to tell them apart. The dashed curve is the transmittance, computed from the transmission coefficients and the two media's projected impedances rather than as one minus the reflectance; it agrees with one minus the reflectance to 4.4e-16 across the whole range, which is where the energy accounting can be seen to close.

A ray meeting the boundary at 56.31°, going from n = 1 into n = 1.5, refracting to 33.69° by Snell's law. The angle between the reflected and the refracted directions is 90.00°, which is a right angle exactly. The light in the second medium sets its charges oscillating along the double arrow, at right angles to the refracted ray for light polarised in the plane of incidence, and the reflected wave is what those oscillating charges radiate. A dipole radiates nothing along its own axis. So when the reflected direction lies along the double arrow there is nothing to reflect, and that happens at exactly one angle: the one where the reflected and refracted rays are square to each other, tan θ = n₂/n₁ = 1.5000.

Degree of polarisation against angle of incidence, for unpolarised light going from n = 1 to n = 1.33. The reflected beam reaches 1 — completely polarised — at the Brewster angle 53.06°, and only there; a degree either side of it and it is already imperfect, which is why a polariser made this way is also a very narrow-angle instrument. The lower curves are what a pile of plates does to the beam that goes through: each plate has two surfaces, and after 8 plates the transmitted beam is 56.6% polarised at the Brewster angle. Reflection throws away most of the light and polarises it perfectly; transmission keeps most of the light and polarises it slowly, and the number of plates needed is the price.

A ray meeting the boundary at 30.00°, going from n = 1 into n = 1.5, refracting to 19.47° by Snell's law. The angle between the reflected and the refracted directions is 130.53°. The light in the second medium sets its charges oscillating along the double arrow, at right angles to the refracted ray for light polarised in the plane of incidence, and the reflected wave is what those oscillating charges radiate. A dipole radiates nothing along its own axis. So when the reflected direction lies along the double arrow there is nothing to reflect, and that happens at exactly one angle: the one where the reflected and refracted rays are square to each other, tan θ = n₂/n₁ = 1.5000.

physicscheck asserts something about fresnel-coefficients 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.