It’s not a palace. It’s the elegant, expansive home and office of a successful professional. It’s packed with stuff displayed with a strategy. It’s part maze, part art gallery, part movie set, part field trip, with a dash of Indiana Jones. It also feels like he’s gone out to get a cup of coffee, leaving us there to explore. It’s that close to time travel.

The museum recently finished a £7 million refurbishment. Soane eventually acquired and renovated three eighteenth century townhouses on Lincoln’s Inn Fields. In keeping with his intention, the buildings are “untouched” but now made suitable for public visits. It’s the most sensitive, delicate, and expensive project. Over time, the innards of the buildings have been updated while the experience of the living spaces stayed as Soane wished.

The show’s a soupçon, with nice renderings of Soane projects like the Bank of England, the Dulwich Picture Gallery, his country house, monuments, and, of course, his London home. It gives us something to think about. Manipulating light is as much of a goal for an architect as shelter and movement. In his Bank of England project, Soane designed a modern space for doing business. It’s 9-to-5 space suitable for clients coming and going during the day but also for stationary office workers. Everyone needed to see what they were doing. Commerce had never been so organized. Well-lit spaces evoked transparency and clarity.

I know the show covers lots of Soane projects, but that’s what we learn about his Bank of England, a massive complex of buildings and his biggest commission. The Bank of England was an icon of British power and the Roman Forum of Britain’s mercantile acumen. Its space was the most reductive Neoclassical architecture, with domes and cavernous spaces and minimal ornament. Light moving across volumes was the one changing dynamic.

Light becomes the Invisible Hand’s totem, moving through the day as capital moves, a force of nature regulated by the Bank as fluidly as light is regulated by Soane’s design. Soane and the Bank of England’s lighting is a fascinating show in itself. “Lumiere Mysterieuse” is, overall, a sampler. That’s not necessarily a flaw in the show. The show is what it is. The bank buildings were demolished in the 1920s, an aesthetic disaster akin to New York’s loss of Penn Station.

Soane’s lighting develops the beauty of his domestic spaces, their elegance and comfort. Filtered light moves gradually and subtly. The lighting during daytime is kept easy and casual. It’s a home, an office, and a studio. No one wants their nerves rattled. Some of the house’s spaces, though, are sublime, not pleasing but unsettling, with a power close to magic. Soane’s art spaces aren’t about comfort but about the ebb and flow of history. Their lighting evokes the emotional and intellectual response Soane wanted.

Soane was a teacher at the Royal Academy, in addition to being a working architect. A lecture drawing from 1812 shows how he lit the house’s Dome Area and shaft of spaces cascading from the dome to the bottom of the house. In these spaces he installed architectural fragments and sculpture spanning centuries, styles, and materials. It’s open storage but it’s also multiple time capsules. It’s a mock excavation boring through the ages. The light is more jarring. We’re watching a drama, and it’s the story of style and discovery over time.

His lighting gives us just the right jolt. We’re seeing very old things bearing the dings of history. Light moves slowly and smoothly here, abruptly there, from harsh to dim and back, each transition working with the objects to get our imagination going. Through light, Soane tells us we can only perceive history, and then only in fragments, some clear, some shadowed. He shows us through light how our perceptions of objects are as incomplete as how we comprehend the past. Like light, our perceptions change, too, as time and culture make some things more important much as light makes them more, or less, visible.

The Dulwich Picture Gallery, designed by Soane in 1817, is the oldest public art gallery in Britain. Soane’s lighting scheme—overhead skylights illuminating a connected set of galleries—became the standard for the emerging genre of public museums for more than a hundred years. Until at least the 1940s, museums in America and Britain were purpose-built and generally inspired by Dulwich. They were illuminated by strategically placed windows, glass roofs, and skylights. Natural light was the rule. Controlled, steady electric light in galleries is newer than many people think.

Most big-city European museums were renovated palaces like the Prado and the Louvre. Architectural drawings show how Soane invented new, imposing, and inspiring spaces where the public, not just kings, aristocrats, and popes, could see and enjoy art. He was among the inventors of modern museum architecture.

The museum commissioned the photographer Helene Binet to make three gorgeous, big photographs of interiors in the house. They’re light studies and very beautiful. They give us a moment to pause and think about Soane and lighting. I would have given her a bigger intervention, or combined her photographs of the house with drawings by Soane and others focusing only on the house’s lighting strategy. A show on lighting design covering many buildings, some long gone, is hard to enliven. It becomes very abstract.

One of London’s most spectacular spaces is the museum’s Picture Gallery. It’s the small space Soane installed with his fabulous paintings and drawings collection. It was widely visited in Soane’s day, and he designed it for public visits when, as he wished, the house opened as a museum. Beautiful works by Canaletto and Hogarth are on view. The walls are layered cabinets. At appointed times, guards ceremoniously open the cabinet doors to show Soane’s gorgeous Piranesi drawings. I think it’s London’s finest art treat.