Malus's law
At its defaults it draws malus's law. The fraction of polarised light passing a filter, against the angle between the light's own direction of shaking and the filter's axis. It is the cosine squared: half at 45 degrees, nothing at 90.
polariser-stack 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.
At its defaults
Drawn even though every essay passes options, because a default nothing exercises is a trap for the next essay to call this with none — which has happened here twice.
The fraction of polarised light passing a filter, against the angle between the light's own direction of shaking and the filter's axis. It is the cosine squared: half at 45 degrees, nothing at 90.
Brewster's angle for n = 1.33: 53.1°
The options are the ones The angle at which reflection picks a side passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Light striking a surface of refractive index 1.33 at 53.1 degrees. The reflected ray leaves at the same angle and the refracted ray continues at 36.9 degrees, so the two are 90.0 degrees apart — a right angle. At that separation the reflected light can only shake perpendicular to the page, and it is completely polarised.
Malus's law
The options are the ones The angle at which reflection picks a side passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
The fraction of polarised light passing a filter, against the angle between the light's own direction of shaking and the filter's axis. It is the cosine squared: half at 45 degrees, nothing at 90.
3 filters at 0°, 45°, 90°: 12.5% gets through
The options are the ones The answer that was not there before passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Unpolarised light passing through 3 polarising filters with axes at 0 degrees, 45 degrees, 90 degrees. The first removes half whatever its angle; each one after it passes the cosine squared of the turn from the filter before. 12.5 per cent of the original intensity survives.
Malus's law
The options are the ones The crystal that answers twice passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
The fraction of polarised light passing a filter, against the angle between the light's own direction of shaking and the filter's axis. It is the cosine squared: half at 45 degrees, nothing at 90.
2 filters at 0°, 90°: 0.0% gets through
The options are the ones The direction of the shaking, and the filter that only asks about it passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Unpolarised light passing through 2 polarising filters with axes at 0 degrees, 90 degrees. The first removes half whatever its angle; each one after it passes the cosine squared of the turn from the filter before. 0.0 per cent of the original intensity survives.
What checks it
physicscheck asserts something about polariser-stack 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.
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.
The angle at which reflection picks a side
At one angle of incidence, a water surface reflects no light at all of one polarisation. The Fresnel algebra says so, and says nothing about why. The reason is that the reflected ray would have to leave along the axis of the charges radiating it — and a shaking charge sends nothing along the direction it shakes in.
QuantumThe answer that was not there before
Send a beam through an analyser and it splits in two. Send one half through a second analyser turned sideways, then through a third pointing the way the first did, and the property the first analyser removed has come back.
QuantumThe correlation no instructions can produce
A pair of gloves in two boxes agrees perfectly and needs no physics, because the answers were settled at packing. What no packing can imitate is the shape that appears as the two analysers are turned relative to each other, and the shape is a number — 2.828 where every list of pre-agreed answers is stuck at 2.
OpticsThe crystal that answers twice
Lay a piece of calcite on a printed page and the print appears twice. One image sits still when the crystal is turned and the other goes round it. Nothing has been done to the light except pass it through a material whose response to a field is not a number.
OpticsThe direction of the shaking, and the filter that only asks about it
A wave that travels one way can still shake in any direction across that way. Light does, most of it shakes in all of them at once, and a sheet of plastic can ask which.
OpticsThe light with no direction of shaking
Unpolarised light is not a state of a wave; it is the absence of one, and no description of a single wave can represent it. What can is a set of four numbers, all of them powers a detector reads — and they describe every beam there is, including the ones that are neither polarised nor not.
OpticsThe pattern the sky is written in
Scattered sunlight is polarised, so the whole sky carries a direction of vibration at every point — arranged in circles about the sun, strongest on the great circle ninety degrees away from it, and vanishing at points that were found by looking before anyone could explain them. Bees navigate by it and a camera filter reads one band of it.
OpticsThe phase that is only a shape
Take a beam of polarised light through a sequence of elements that returns it to the polarisation it started with, and it comes back with a phase it did not have before. That phase is not an optical path length — it does not depend on the thickness of anything, or on the wavelength, or on how slowly the sequence was carried out. It is minus half the area the path enclosed on the sphere of polarisation states, and nothing else.
OpticsThe retarder with no crystal in it
A wave plate turns linear polarisation into circular by making one component travel a little further than the other, which requires a birefringent crystal cut to a thickness and works properly at one wavelength. Total internal reflection does the same job with a phase that comes from the geometry instead — and because a refractive index barely changes across the visible where a wavelength changes by a factor of two, the same block of ordinary glass is a quarter-wave plate for every colour at once.
OpticsThe rotation a return trip doubles
Quartz turns the plane of polarisation and so does glass in a magnetic field. The two look identical on the way through and are opposites on the way back — the crystal undoes its own rotation exactly, and the magnet adds to it. That difference is the whole of why a one-way street for light can be built at all, and why nothing passive will ever be one.