When 1,633 delegates to the Democratic midterm convention sit down in Memphis Friday night to watch a movie extolling President Carter, they will be seeing, in part, a documentary on the power of political incumbency, brought to them courtesy of the U.S. Navy.

The White House and the Democratic National Committee have made extensive use of official government film footage shot by Navy cameramen in producing the motion picture that will precede Carter's speech to the convention.

Rod Goodwin of Magus Corp. the private film company hired by the DNC to produce the film, said yesterday that about a third of the 14-minute production will consist of footage shot by Navy camera crews assigned to the White House to record the president's public activities.

There are no legal prohibitions against use of the film for partisan political purposes, according to Pentagon officials who said they considered that the Navy footage is available to the public.

But use of the government film, which is stored at the Naval Photographic Center and eventually will be turned over to the Carter presidential library in Georgia, resulted in a substantial savings in production costs to the DNC and gave the filmmakers access to the most complete photographic record available of Carter's first two years in office.

What the convention delegates will see in Memphis is not the original Navy film but copies of it produced in a commercial laboratory by a process known as "mastering." According to Denny Pilgrim, head of the firm that made the copies for Magus, the technique is up to 10 times less expensive than producing original film.

DNC Chairman John White told reporters Thursday that the party is spending about $65,000 to produce the film. It was first suggested about a year ago by Gerald M. Rafshoon, Carter's assistant for communications, who wanted it to be produced by his own advertising agency.

Since then, Rafshoon has moved to the White House, so the project was turned over to Magus, which, under contract to Rafshoon's agency in 1976, had produced film for the Carter campaign's television commercials.

Goodwin said Magus borrowed about 100,000 feet of film from the Navy, from which the producers culled about 8,000 feet that was processed by Pilgrim's firm. Some of this footage was edited into the final production, entitled "A Democratic Partnership" and narrated by actor E. G. Marshall.

Jack Horton. head of the naval film unit, said the Navy will be paid for any costs to it in locating the film sought by Magus. He said he did not recall former president Ford making similar use of Navy footage in his campaign.

Technically the film belongs to the Navy, but access to it is controlled by the White House. Anne Edwards, White House television coordinator in Rafshoon's office, said she never thought twice about allowing Magus to use the film.

"I considered it public access stuff," she said, adding that the White House routinely approves use of Navy footage film by documentary filmmakers, educational organizations and others. Edwards said she has approved use of the Navy film by a few Democratic political candidates, but has had no requests from Republicans.

Rafshoon also defended use of the government film at a Democratic function. "That's stock footage that can be bought by anyone," he said.

Asked if the White House would allow the Republican National Committee to use the film to produce a presumably critical movie about Carter, he replied, "Absolutely."