Tim Jenison, right, adjusts the wig of model Graham Torns in Tim’s Vermeer (Shane F. Kelly/Sony Pictures Classics)

Hailing from the Iowa cornfields, high school graduate, self-taught techie inventor, and self-made millionaire Tim Jenison turns his life over to a wonky but accessible pursuit. He spends his considerable resources and time traveling the world scrutinizing Dutch superstar painter Johannes Vermeer (1632–75). His mission: to the find the secret to Vermeer’s photographic, starling life-like paintings. In particular, he attempts to duplicate The Music Lesson, now owned by Queen Elizabeth.

Any skepticism that this breezy documentary-as-mystery is a vanity project is dispelled early on when Jenison delves into how Vermeer created his 34 (the number varies) works now known to exist. The film leaves it to biographers for the painter’s life story, like his neglect and then his rediscovery in the 19th century.

Jenison learns Dutch, travels to Vermeer’s hometown of Delft, in the Netherlands, and even scores a private 30-minute viewing of the painting in Buckingham Palace (no, the camera was not allowed within). He also brings the big guns for his investigation, namely painter and chain-smoker David Hockney, who proposed in his 2001 book Secret Knowledge: Rediscovering the Lost Techniques of the Old Masters that Vermeer was aided by technology to create his allusion of perspective.

Taking this as a starting point, Jenison adapts an advice, a modified camera obscura—a box-like optical device with a small aperture that projects images onto a flat surface—with the use of concave lens and mirrors. Art historian Philip Steadman purports here and in his book Vermeer’s Camera: Uncovering the Truth Behind the Masterpieces that Vermeer used such technology to trace images.

Jenison chooses to replicate the interior setting of The Music Lesson (circa early 1660s) in his San Antonio studio, constructing the room in the painting artisanal style, using only natural light. He crafts by hand all of the props (after all, a 17th-century viola de gamba is hard to find). His daughter, home from college, poses as the woman at the keyboard instrument, her back to the viewer, with a dapper gentleman—her teacher, perhaps—as her attentive audience of one. (After standing still for days on end, she’s more than ready to go back to class.) In the film’s equivalent of the “smoking gun,” Jenison discovers a flaw in Vermeer’s painting—and a remarkable coincidence.

The viewer will watch paint dry and like it. Impressively, Jenison captures the intricacies of the objects, and for someone who has never previously dabbled in painting, he’s more than a capable draftsman, and through his device, he matches the colors of his models and the set. However, he doesn’t replicate Vermeer’s “It” factor, how the original painting glows with, as Jenison calls it, a “magical quality,” as though Vermeer “painted with light.” Other mysterious matters that Jenison touches upon are the secret formulas for grinding and mixing paint and how the lenses were manufactured—and by whom. That’s another conundrum.

Step by step, he and the filmmakers, his friends and magicians Penn and Teller, lay out their theory credibly, leaving it for the viewer to accept or dismiss. Though they propose that the work Girl with a Red Hat is another example of the painter employing then-cutting edge science, they refrain from probing further, allowing plenty of room for speculation, like why Vermeer’s sense of proportion in a later painting, The Allegory of Faith, now at the Metropolitan Museum of Art, is out of alignment. The bulky figure of the woman representing Catholicism is distorted in comparison to Vermeer’s subtly dramatic domestic tableaus. In this religious painting (perhaps made for a Catholic patron, but, really, who knows?), the Amazon’s feet are giant size, and her shoulders and arms brawny and broad. Nor is there a comparison of Vermeer’s contemporaries, many of whom were also based in Delft. Regardless, the film will likely win over some converts, and Conrad Pope’s elegant Satie-inspired score offers a laid-back and seductive accompaniment to this art world what-if.