The 1937 Roanoke Colony Memorial Half Dollar was struck to commemorate the "three hundred and fiftieth anniversary of Sir Walter Raleigh's colony on Roanoke Island, North Carolina, known in history as the Lost Colony, and the birth of Virginia Dare, the first child of English parentage to be born on the American continent.
1937 Raleigh Colony Memorial Half Dollar

1587 was not, however, Raleigh's first attempt at establishing a New World colony. Raleigh financed an expedition of exploration along the present-day North Carolina coast in 1584, and attempted to establish a colony on Roanoke Island in 1585. (Raleigh financed these endeavors, he did not physically take part in either expedition.)
In 1935, the William L. Clements Library (of the University of Michigan) held one of the more academically-oriented commemorations of Sir Walter Raleigh's initial attempts to colonize the New World in 1585. On the 350th anniversary of the second New World voyage sponsored by Sir Walter, the Clements Library staged an exhibition titled "Raleigh's Roanoke Colony of 1585."
Note: The Clements Library was founded in 1923 and specializes in rare books and manuscripts with a focus on the history of North America and the Caribbean. Clements Library "Ralegh" Exhibition Program Cover
The exhibition was driven by selections from the library's collection of rare books that recorded the early history of America and its colonization activities. The core of the exhibition was a book first published in 1588:
A Briefe and True Report of the New Found Land of Virginia; 18 copies of the book were on display within the exhibition (more on this below). The book was written by Thomas Heriot, a farmer who was among the colony's first settlers in 1585; the original edition of the book was published in London, England. (At the time of Raleigh's Colony, the area was referred to as "Virginia" (named so by Raleigh) in honor of Queen Elizabeth (the "Virgin Queen"). It would not be until 1663 that the "Province of Carolina" would be considered separate from the "Province of Virginia" and not until 1712 that "North Carolina" and "South Carolina" were delineated.)
The Heriot book features 23 engravings by Theodor de Bry; the engravings were based on the paintings of John White. White was part of the 1585 expedition to establish the colony at Roanoke.
The exhibition included 17 of the 23 de Bry engravings. Why just 17? The Clements Library had copies of 17 different follow-up editions of the Heriot book that were published in the decades that followed the original in 1588 and used each of them to present a different engraving.
The Library published a small guide to the exhibition (it printed 1,000 copies) that introduced the books and artwork included in its display. Shown below are the cover, title page and timeline page from the booklet; also presented is the portrait of Sir Walter Raleigh that was included in the Guide and exhibition.
The University of North Carolina, as part of its "Documenting the South" initiative has posted the text of Heriot's original volume along with its original engravings. I've included two images here (they are in the public domain) but suggest visiting the UNC site to read the book's text and to see all of the engravings. You can access it here:
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A Briefe and True Report of the New Found Land of Virginia.
I realize that this exhibition does not have a direct tie-in to the Roanoke Colony commemorative half dollar, and even focuses on the initial colonization attempt of 1585 vs. the 1587 attempt commemorated by the coin, but I find it an interesting piece of background for the coin and thought others might also appreciate it.
Clements Library "Ralegh" Exhibition Program - Title Page
Clements Library "Ralegh" Exhibition Program - Sir Walter Raleigh Portrait
Clements Library "Ralegh" Exhibition Program - Timeline PageIf you're looking for a condensed "Events Schedule" for Raleigh and his attempts at a Roanoke Island colony...
Theodor de Bry Engraving: Arrival of English - Watch Out for the Sea Serpent!
Theodor de Bry Engraving: Chief Roanoc
For other posts about commemorative coins and medals, including many on the Roanoke half dollar, see:
Commems Collection.