MAKE no mistake, the interns are fighting back.

Last month, a federal judge in New York ruled that unpaid interns on the movie “Black Swan” should have received at least the minimum wage. The judge also allowed a class-action suit to go forward against the Fox Entertainment Group, the parent company of the film’s production division.

Gutsy and improbable when it was first filed two years ago, the “Black Swan” case was a pioneering direct challenge to the internship system. Now more than 15 other lawsuits have followed in its wake, according to an online database maintained by ProPublica, the investigative journalism Web site.

The companies being sued operate in a wide range of intern-heavy industries. Global brands, famous television and fashion personalities, multinational subsidiaries flush with profits — these are some of the employers that have refused to pay young workers at least $7.25 an hour. How have they done this for so long?

The federal law is clear: if internships at profit-making companies are to be unpaid, they must foster an educational environment. (The rules are different for nonprofit and governmental agencies.)