A middle-aged couple sits in a New Jersey cottage that’s utterly ordinary — except that it’s in a nudist colony, and its inhabitants are naked. A close look at the family snapshots perched atop the TV reveals that the people in them are unclothed, too.

What can’t be seen in this 1963 photograph is that the woman who made it was also naked. Diane Arbus went to extremes to explore society’s outer limits.

Arbus’s photographs of physically, psychologically or philosophically unusual people have been called exploitative or sensationalistic. But in making her pictures, the New York photographer showed empathy, understanding and perhaps even a sense of identification with her subjects. The degree to which Arbus saw herself in her subjects is a matter of ongoing conversation. But her July 1971 suicide suggests that she did feel, in some way, an outsider.

“Diane Arbus: A Box of Ten Photographs” recounts the stories of the artist, her subjects and the portfolio she conceived barely 18 months before her July 1971 suicide. The show also tells something about the institution that’s hosting it, the Smithsonian American Art Museum, and its relationship to Arbus’s career. In addition to the photos once contained in a clear Plexiglas rectangle, the display includes numerous documents, explanatory text and several images of Arbus made by others.

Arbus began as a fashion photographer — her parents ran a chic Fifth Avenue department store — and then moved toward street shooting. In her mature work, she fused the two. Her subjects are singular and unglamorous; even the drag queen in this selection is not yet in full finery, with hair still in curlers. But the people are carefully posed and crisply rendered, shot with a large-format camera and often frozen with a strobe. The resulting pictures are stolen glances and formal portraits at the same time.

The pictures from 1962 to 1970 that Arbus chose for the box, limited to an edition of 50, include some of her most famous: The nudist couple. The young twin girls, one glaring while the other smiles gently. The men Arbus described as the “Mexican dwarf” and “the Jewish giant.” Also included are a smoldering pro-war demonstrator, sporting a straw hat and a “Bomb Hanoi” button, and a young Brooklyn couple with their two kids, very domestic while retaining their tough-teen fashion sense.

Arbus sold only four of the portfolios before her death, and personalized each one. The set the Smithsonian museum bought in 1986 was originally purchased by Bea Feitler, the Harper’s Bazaar art director who later helped found Ms. magazine. Arbus added an 11th print for Feitler, a friend: a woman with a fully dressed baby monkey on her lap. (Photographer Richard Avedon also got an extra print in his box.)

While Arbus’s work still elicits a range of strong responses, her significance as an artist is seldom questioned. In 1971, however, both the photographer and her medium were considered suspect. That’s the other part of the box’s story: It changed the way photography was regarded, and treated.

When the portfolio was featured in Artforum in May 1971, it was the first time the magazine had spotlighted a photographer. A year later, in June 1972, one of the boxes was dispatched to Italy, where Arbus was the first photographer ever included in the Venice Biennale.

To bring the tale back to the building where the 11 pictures are now on display, it was the Smithsonian’s American art museum (then called the National Collection of Fine Arts) that chose the U.S. art for that year’s Biennale. The curator in charge of the selection was Walter Hopps, a near-legendary D.C. art scene figure. Five months later, the Museum of Modern Art opened an Arbus retrospective that clinched her reputation.

Since those breakthroughs, photography has become a museum mainstay while moving far from Arbus’s stark, observational black-and-white style. And the artist has partly merged into her myth, as imagined in 2006’s “Fur: An Imaginary Portrait of Diane Arbus” (with no less than Nicole Kidman in the title role).

The Smithsonian show takes a less romanticized view. It depicts Arbus as a teacher, an artist, a woman who worried about money. But she was capable of entering another dimension, one whose eeriness is only amplified by its reality. “A Box of Ten Photographs” is a stroll down the sideshow of the everyday.

If you go

Diane Arbus: A Box of Ten Photographs

Smithsonian American Art Museum, Eighth and F streets NW. 202-633-7970. americanart.si.edu.

Dates: Through Jan. 27.

Admission: Free.