Public approval of President Reagan's handling of his job has rebounded to its highest level in nearly 18 months, according to a Washington Post-ABC News poll, which shows his rise in popularity clearly tied to a growing perception that the nation's economy is improving.

More people view Reagan positively now than in any Post-ABC News poll since November, 1981, and fewer view him negatively than in any since January, 1982. The turnaround has occurred since this January.

The new poll shows 53 percent saying that they "approve of the way Reagan is handling his job as president" and 42 percent saying that they disapprove. In January, the figures were almost exactly reversed, with 42 percent saying that they approved and 54 percent saying that they disapproved.

At the same time, however, various groups of Americans remain sharply polarized in their views toward Reagan, with some looking at him extremely favorably and others extremely harshly. Relatively few take a middle ground.

If the popularity rating were likened to a person's body heat, Reagan might be viewed as having his head and shoulders in a refrigerator and his legs in an oven, while registering a healthy overall temperature. In addition, there is still majority disapproval of important, specific aspects of the Reagan presidency, including his handling of unemployment, his proposed cuts in social programs and his administration's fairness.

One question in the survey asked: "Would you say Reagan cares more about making things better for the majority of the American people, or does he care more about serving a few special interests?"

A majority, 52 percent, said that the president cares more about special interests. Among them, 69 percent disapprove of Reagan's handling of the presidency and 25 percent approve.

Forty-three percent say that Reagan cares more about the majority. Among them, approval of Reagan is overwhelming, with 9 in 10 giving him a favorable job rating.

Among other sharp divisions:

* Those with annual household incomes of $30,000 or more approve of Reagan's performance by 68 to 29 percent. Those with incomes of $12,000 or less disapprove by 55 to 39 percent.

* Whites approve of his performance by 58 to 37 percent. Blacks disapprove by 74 to 18.

* Men approve of Reagan by 60 to 36 percent. But women are evenly divided, with 47 percent approving and 46 percent disapproving.

* People who describe themselves as belonging to the middle class approve of Reagan by 62 to 34 percent. Among those who say they belong to the working class, 47 percent approve and 47 percent disapprove.

Most of those divisions represent little change in sentiment toward Reagan over a long period of time. Almost since the beginning of his presidency, polls have noted sharp polarization of the public in its views toward him.

But, as the perception that the economy is improving becomes more widespread, Reagan has made at least some gains even among groups most disdainful of him. Democratic voters, for example, rated Reagan negatively by 77 to 20 percent in January; now they disapprove by 64 to 29 percent.

In the poll, conducted by telephone nationally from May 11 to 15, more than 4 in 10 said that they feel the nation's economy is getting better. That is a slight increase over April and March, but more than double the belief in recovery found in all earlier Post-ABC News polls since Reagan became president.

In addition, fewer than 1 in 5 said they feel that the economy is getting worse, a sharp decrease since the beginning of the year.

Among those who take the optimistic view of the economy, 3 of every 4 said that they approve of Reagan's handling of the presidency. Among those who are pessimistic, 3 of 4 disapprove.

The poll shows scant change since April in views on the 1984 presidential campaign. Reagan leads former vice president Walter F. Mondale by 47 to 42 percent among registered voters and is even with Sen. John Glenn (D-Ohio), at 44 to 44.