"Tim's Vermeer," a fascinating documentary by the comic magicians Penn & Teller, has a way of arousing passionate feelings while provoking fresh ideas about the porous border between technology and art.

The film was produced by Penn Jillette and directed by Teller in his feature debut. It's serious in purpose, an inquiry into how the 17th-century Dutch painter Johannes Vermeer was able to achieve his mysteriously dense, almost photorealistic detail—seemingly suffused with an inner glow—long before the invention of photography. But the scholarship is enlivened, sometimes hilariously, by showmanship. At certain points the inquiry takes on the trappings of an elaborate magic trick performed by the movie's guru and genial star, a computer-graphics virtuoso, video-software inventor and multimillionaire tinkerer named Tim Jenison.

With nothing up his sleeves ("I'm not a painter," he keeps telling us), Mr. Jenison demonstrates how the 17th-century Dutch master might have gone about creating his singular scenes (with mirrors, as befits a magician of any century, plus lenses that were widely available in the Holland of that time). He does so by using elegantly simple technology that Vermeer might have used—the key word is might—to paint his own version of "The Music Lesson," a beloved masterpiece by one of the most revered figures in the pantheon of Western culture. No connoisseur would mistake Mr. Jenison's Vermeer for the real thing, but his handiwork makes a strong case for the ingenious speculations that informed his amateur effort.

This isn't the first time someone has suggested that Vermeer employed optical tools along with his brushes, pigments and canvas. More than a decade ago the contemporary painter and photographer David Hockney, among others, proposed that many of the Old Masters, including Vermeer, used a camera obscura—essentially a big pinhole camera—fitted with a lens to focus images of their subjects on canvas, then traced the outlines before filling in the details. But Mr. Jenison carries the proposition much further. His method involves a 45-degree-angle mirror, not much larger than the kind used by dentists, on a movable stand. Positioned between projected image and canvas, the comparator mirror, as he calls it, allows him to duplicate colors, as well as outlines and details, in one small area after another. This is bound to sound abstruse in the telling, but it's perfectly clear in the showing, and only the beginning of a process that qualifies Mr. Jenison as a New Master of obsessive-compulsive devotion.

That's because of the lengths he eventually goes to during eight years of study, preparation and execution. He doesn't copy from the original, with its daylight-bright room in which a young woman stands at a harpsichord, her male teacher alongside her. That would have been impossible in any case, since Queen Elizabeth II has "The Music Lesson" under protective custody in Buckingham Palace. Instead, he spends 213 days building a full-scale replica of that venerable room, and its contents, in his warehouse in San Antonio. (The process is considerably compressed in a film that runs 80 minutes.)

At the same time, he learns to mix pigments as the artist would have done, and makes his own lenses. Then, with the help of his trusty mirror, he spends another 130 days reproducing projected images of the replica on canvas, area by area, detail by painstaking detail. "It's possible," Mr. Jenison says, that Vermeer "was more of an experimenter, more of a tinkerer and more of a geek, and in that way I feel a kinship with him. Because I'm a computer-graphics guy, and we use technology to make beautiful images."

The experiment is spellbinding, though some of the commentary is opaque, or at least incomplete. We are told, for example, that the human retina's limited bandwidth would have made it impossible for Vermeer to capture the gradations of certain areas of his canvas without optical aids. How come? The areas in question don't look unusual, and fine artists capture extraordinary nuance as a matter of course. There's an odd, though perhaps inadvertent, omission in a key scene when the computer-graphics-guy-turned-painter shows Mr. Hockney his finished faux-Vermeer, and the equipment he used to paint it. Mr. Hockney is greatly impressed by the accomplishment: "I think it might disturb quite a lot of people," he says with wry pleasure. But we never see Mr. Hockney being told about, let alone reacting to, the crucial role of the angled mirror. And the film could have done without Mr. Jillette's enthusiastic overstatement—showmanship eclipsing scholarship—that "my friend Tim painted a Vermeer in a warehouse in San Antonio. He painted a Vermeer."

No, he didn't. He painted a painting that demonstrated a kind of proprietary hardware Vermeer might have used. Still, the enterprise was disturbing enough for friends I took to the screening—a prominent architect and educator, and his equally sophisticated wife. They were furious at what they saw as a debunking of the Vermeeer mystique, and they insisted, at least for a while, that the whole thing was bogus, or that someone with a more practiced hand than Mr. Jenison's was wielding the brush that, with the help of lenses and mirrors, produced a Vermeerish minorpiece.

But "Tim's Vermeer" isn't debunkery, and the value of the process it documents doesn't depend on the quality of Mr. Jenison's final product, even though his painting looks impressive to my limited-bandwidth eyes. His experiment should be seen as an attempted—and impressive—proof of concept, while the film proves, yet again, the vitality of the documentary form. The most intriguing question it raises is whether our feelings about Vermeer may be changed by the likelihood of him having used optics of one sort or another. The answer is yes, unavoidably, but not necessarily for the worse. Living in this era of explosive growth in science and technology, it's easy to feel a kinship with an artist who used every tool at his command in the service of beauty.

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