A selection of the 50p coins will also include what the Royal Mint called a “groundbreaking caustic feature”.
“When light strikes the surface of the coin,” it said, “a hidden image is revealed, the all-seeing eye of Sauron, emerging from the negative space at the centre of the Ring.
The feature is designed to “focus light in a precise and deliberate way, projecting the image of the eye of Sauron onto a target surface”.
“This is the first time caustic technology has ever featured on a UK coin available to the public making it a truly unique collectable,” it added.
“Even the most devoted fellowship of collectors couldn’t have imagined a coin quite like this,” said the Royal Mint’s Rebecca Morgan.
“It’s a remarkable feat of British craftsmanship, and one that fans will have to see to believe.
“Whether you’re a lifelong fan or a dedicated collector this is one coin you absolutely will want to own.”
The first coin in the series goes on sale at 09:00 BST on Wednesday.