The very word “Bollywood” conjures visions of peacock blues, turmeric yellows and rose pinks; the pounding drumbeat of bhangra; and dancers whose hip-shaking defies the laws of physics. With its name, “Beyond Bollywood: Indian Americans Shape the Nation,” now at the National Museum of Natural History, certainly trades on such exotic notions. Its focus, however, is the legacy of Indian Americans whose connection to their motherland and to those hip-shakers is not always a given.

Organized by the Smithsonian’s Asian Pacific American Center and on view in a sizable space on the museum’s second floor, “Beyond Bollywood” is immaculately and immersively designed. Walls are splashed in hues inspired by spice markets and South Asian textiles, music is piped in overhead and the subject matter is presented so appealingly that other exhibitions with an anthropological bent would do well to mimic it.

The curatorial steward of all this is Masum Momaya, who arrived at the Smithsonian largely to fulfill the exhibition’s promise.

Her task was daunting. The Smithsonian, she says, had nothing in its vast collections (estimated at 137 million objects) to fill “Beyond Bollywood.” So the Asian Pacific American Center placed an open call for objects and documents related to Indian Americans, a call that led to, among other things, the installation of shoes and family photos that serves as the exhibit’s welcome. (The forthcoming Museum of African American History and Culture also scouts for items in this way; it’s a strong plan for piecing together historical narratives that might be lost.)

After its homey welcome, the exhibit divides the Indian American experience into a handful of sections, including one that looks at migratory tales that stretch back to the 1800s, when farmers from the northwestern Indian state of Punjab arrived to work in the burgeoning agricultural industry of California, Oregon and Washington state, to build railroads and to labor in lumber mills.

The turban-wearing newcomers weren’t necessarily welcomed. To discourage them from staying, U.S. policy made it hard for them to bring wives and other family members. Frequently, however, they did stay, sometimes marrying Mexican women and spawning Punjabi Mexican families whose footprint is still seen on the West Coast today.

For those who know Indian Americans mostly from the second wave of immigration, which began in the 1950s and ’60s and brought a highly educated population of scientists, doctors, engineers and students to the United States — the wave my own parents rode in on to Philadelphia in 1973 — it’s worth spending extra time poring over the newspaper articles and photos in this section of “Beyond Bollywood.” These early immigration stories, documenting the violent reception “Hindoos” received and the ways in which it sparked civic activism, are rarely discussed outside ethnic studies courses.

“Beyond Bollywood” is best, in fact, when it casts light on Indian Americans’ struggles to fit in in their new homeland.

Consider Chiraag Bhakta’s series of photographs of motel owners and their families. The photos capture how family and religious life perseveres even in small-town Super 8s. In stark scenes of elderly parents and youngsters who help maintain the hotel, living out of its rooms in some cases, these photos also expose, perhaps better than anything in “Beyond Bollywood,” the class disparities that divide Indian Americans. Nearby, a sliver of a documentary following a Sikh cab driver in San Francisco (strangely, its screen is part of an art installation resembling a cab with New York plates) also conveys an aching loneliness, particularly when the subject confesses that his Indian classmates and friends would be surprised if they knew he had come to America to drive a cab.

Contrast these downbeat images with the vexingly positive approach that “Beyond Bollywood” takes elsewhere. Naeem Khan’s one-shouldered dress worn by first lady Michelle Obama is lovely, and gymnast Mohini Bhardwaj’s 2004 Olympic silver medal is impressive. But a highly self-congratulatory section devoted to spelling bee winners and a wall of fame featuring such high-profile Indian Americans as actress Mindy Kaling and former NFL player Brandon Chillar feels like a low point, seeming not to tell a broader story of South Asian immigrants so much as to point out brown faces doing surprising things.

It’s also impossible not to notice the subcontinent-size folly of the Smithsonian’s show: For the extraordinary amount of space — 5,000 square feet — there are astonishingly few objects.

Among the most compelling is a turban worn by Balbir Singh Sodhi, a Sikh gas station owner in Arizona who was shot to death four days after the Sept. 11, 2001, attacks, in a killing apparently intended to avenge the terrorists’ victims. (In 2003, Sodhi’s killer, Frank Silva Roque, was convicted of first-degree murder.) The presence of the turban, recently added to the collection of the National Museum of American History, filled me with a familiar, visceral wave of dismay. Like Trayvon Martin’s hoodie, it may someday serve as a reminder that we forget incidents such as these far too easily.

A question nagged at me as I walked through “Beyond Bollywood”: What do I really gain from an exhibit that feels at times like an extended look in the mirror? Is it satisfying to see my mother’s Corelle plates, the very same ones I loathed as a teenager, in the hallowed halls of a museum? For me, it’s anything but.

Corelle doesn’t belong here, mere feet from dinosaurs and great beasts whose existence is mind-boggling. And if ticking off our achievements is all that Indian Americans have to say about our own history, perhaps we don’t belong in a museum yet, either.

It’s worth noting that the $1 million “Beyond Bollywood” exhibition was the brainchild of a group of Indian Americans who approached the Smithsonian. The exhibition, too, was largely bankrolled by members of the community in California, Atlanta and elsewhere.

On a cynical day, I might argue that their influence, both financial and in the images prominently displayed in the exhibit, makes “Beyond Bollywood” feel like a vanity project. Its audience — far broader than this exhibit seems to recognize — deserves better.

Beyond Bollywood: Indian Americans Shape the Nation

Through Aug. 16, 2015, at the National Museum of Natural History, 10th Street and Constitution Avenue NW. (Metro: Smithsonian). 202-633-1000. Open daily 10 a.m. to 5:30 p.m. Free.