A polariser darkens a blue sky and kills reflections off water, glass and wet foliage by passing light vibrating in one plane and absorbing the rest. On the scene side of the lens a linear and a circular polariser do the same job: both hand linearly polarised light to the front element, and both give the identical tonal effect on a sheet of HP5+ or FP4+. The difference lives entirely inside a camera that samples the beam before it reaches the film.

One equation behind all of it

The governing law is Malus’s law: the intensity transmitted through a second polariser set at angle theta to the first is I = I₀ cos²(theta). At theta = 0 the axes are aligned and transmission is maximal; at theta = 90 degrees the axes are crossed and ideal transmission is zero (real polarisers leak somewhere between 10⁻⁴ and 10⁻⁶, set by their extinction ratio).

That single cos² term does two things at once. Rotate the filter on the front of the lens and you change the angle between its axis and the partially polarised light coming off the sky, so the sky darkens and lightens as cos² of that angle. The same term governs the trouble inside the camera: a linear polariser on the lens becomes the first element of a crossed pair, with the camera’s metering or AF beam-splitter as the second. As you rotate the filter, the throughput to that internal sensor swings with cos² of the angle between the two — quite independently of the actual scene luminance.

How an SLR samples the beam

An autofocus SLR does not send all the light to the film. The main reflex mirror is partially silvered; the fraction that passes straight through it strikes a small secondary mirror mounted behind it, which folds the beam down to the phase-detection AF module in the base of the body. There, separator lenses take rays from opposite edges of the lens’s exit pupil and form two images on a linear CCD. The separation between those two images encodes focus error: too close together and the subject is front-focused, too far apart and it is back-focused, a fixed reference gap when focus is true.

Both the secondary mirror’s dielectric coating and the separator optics reflect and transmit by amounts that depend on the polarisation state of the light. Feed them a clean linear polarisation and the relative intensities of the two split images shift with filter rotation. The phase comparison is reading an intensity imbalance the optics imposed, not the actual defocus, so focus drifts. The same mechanism corrupts a beam-splitter exposure cell: as camera-wiki puts it, with a linear polariser fitted “both exposure meter and auto focus will not work properly.”

The quarter-wave plate, and why it faces the lens

A circular polariser is a linear polariser bonded to a quarter-wave plate — a lambda/4 retarder — with the retarder’s fast and slow axes at 45 degrees to the polariser’s transmission axis. Light leaves the front polariser linearly polarised, then the retarder delays one of the two orthogonal field components by a quarter wavelength, a 90-degree phase shift, relative to the other. The two components recombine as circularly polarised light.

The point of that trick is that circularly polarised light presents equal amounts of both linear states to any downstream analyser, at every rotation of the filter. The cos² term that swung with angle now averages to a constant: a beam-splitter divides circular light exactly as it divides unpolarised light, so the meter and AF module behave as if no polariser were on the lens. The scene-facing polarisation — sky, reflections — is untouched, because that work is done by the linear element out front. The order matters, which is why a CPL is directional: the retarder must face the lens. Mount one backwards and you hand the beam-splitter linear light again.

When circular polarisers appeared, and why

The fix exists because of a specific change in camera design. So long as a body metered with a non-beam-split cell or you read an external meter, a linear polariser was fine. The problem arrived with beam-splitter AF and TTL bodies, beginning with the Minolta Maxxum/Dynax 7000 in February 1985, the first SLR with a fully integrated in-body autofocus system and motorised film advance. As polarisation-sensitive secondary mirrors and AF/metering optics spread across the market, the circular polariser became the default recommendation. On a fully manual, mechanical body with handheld metering, a linear polariser is still perfectly usable, and it is typically cheaper with very slightly higher transmission.

What it costs in light, with a worked example

The filter is not free, but the common “one to three stops” folklore is too loose and the top end is wrong. It double-counts: the angle-dependent darkening of an already polarised sky is a scene effect you chose, not the filter’s base attenuation. Manufacturer data is much tighter. Heliopan rates a filter factor of about 2.3 to 2.8, roughly +1.3 stops; B+W Kaesemann circular polarisers sit in the same range, and the HTC (High Transmission Coating) Kaesemann reaches about 99.5 percent transmittance per polarised component, quoted at up to about 1.5 stops.

With TTL metering and a CPL on the lens you apply nothing by hand: the meter reads the same attenuated beam the film sees. With a handheld meter you apply the factor yourself. Say you are metering a Zone V midtone on FP4+ and your incident reading gives EV 14, which you would set as f/11 at 1/125 s. Fit a Kaesemann and open up its +1.5 stops: about f/6.7 at 1/125 s (halfway between f/8 and f/5.6), or hold f/11 and drop to 1/45 s. There is one wrinkle a meter cannot see for you. A polariser’s effect on the sky peaks when the camera points 90 degrees away from the sun and fades toward zero pointing at or directly away from it, so the effective factor creeps higher as you rotate toward maximum effect on a clear sky 90 degrees off-sun. When in doubt, bracket a stop either side.

Is it even worth it on black-and-white film?

For the headline trick — darkening a blue sky — a polariser is usually the wrong tool in black-and-white. Coloured contrast filters do it better and more controllably, because they act on colour rather than angle: a Wratten 25 red, 15 deep yellow/orange, or 12 minus-blue darkens sky predictably wherever you point the camera. Ansel Adams reached for a Wratten 29 deep red, not a polariser, for the near-black sky of Monolith, the Face of Half Dome (1927). A polariser darkens any blue sky regardless of which contrast filter you also use, but its real value in black-and-white is killing non-metallic reflections off water, glass and wet leaves — reflections no coloured filter can touch. That is when its stop-and-a-half is worth spending.

Sources: HyperPhysics (Georgia State University) on the quarter-wave plate; Harvard Natural Sciences Lecture Demonstrations on Malus’s law; camera-wiki.org and Lensrentals on phase-detection AF and beam-splitters; Heliopan and Schneider-Kreuznach/B+W datasheets for filter factors; Wikipedia and mikeeckman.com on the Minolta Maxxum 7000; Ansel Adams, The Negative.