President Barack Obama makes a cameo appearance on “Mythbusters” (8 p.m., Discovery) tonight. Hosts Jamie Hyneman and Adam Savage visit the president in the White House, where he praises the show for its entertaining celebration of science and experimentation and asks the guys to revisit a project from the show’s past.

President Obama doesn’t think they tried hard enough to prove or disprove the legend of the ancient Greek scientist Archimedes, who is said to have instructed troops to set fire to an invading Roman fleet using only mirrors and the reflected rays of the sun. Adam and Jamie return to the project, equipped with 500 mirrors and an “army” of 500 high-school students eager to reflect new light on the old story.

By appearing on “Mythbusters,” the president reaffirms his support for science education but walks a rather fine line. Is he right in reaching out to people via a fractured cable audience? Or is he demeaning the majesty of the office on a goofy show where stuff often gets blown up?

During a recent “60 Minutes” interview, President Obama argued that appearances on cable shows, or morning shows like “The View,” were required to reach the folks who no longer watch more traditional outlets (like “60 Minutes”).

Presidential outreach has often brought mixed reviews. Jimmy Carter once fielded odd questions on a radio talk show. Bill Clinton was asked about less-than-dignified matters by an MTV correspondent and once sat down on VH1 to discuss his record collection and musical influences.

If cable still seems a strange place for a sitting president, it has certainly become an outlet where people launch their presidential campaigns. Ross Perot began his 1992 bid on “The Larry King Show.” Pat Buchanan used his “Crossfire” perch to unleash insurgent primary campaigns in 1992 and 1996.

Tonight’s other highlights

• Eight groups contend on “The Sing-Off” (7 p.m., NBC).

• Chance turns to an unlikely savior on “Human Target” (7 p.m., Fox).

• Frankie’s parents (Marsha Mason and Jerry Van Dyke) arrive for the holidays on “The Middle” (7 p.m., ABC).

• School-dance jitters on “Modern Family” (8 p.m., ABC).

• The guys count down viewers’ favorite clips from the past season and anticipate the next on “The Fabulous Beekman Boys Holiday Special” (8 p.m., Planet Green).

• “Marijuana USA” (8 p.m., CNBC) examines an enormous underground marketplace.

• The 1988 documentary “Imagine: John Lennon” (8 p.m., BBC America) recalls the singer-songwriter on the 30th anniversary of his murder.

• A gunrunner seeks counsel on “The Defenders” (9 p.m., CBS).

• A freed suspect becomes an asset on “Law & Order: SVU” (9 p.m., NBC).

• A psychic seems to know too much on “The Whole Truth” (9 p.m., ABC).

• Police-academy high jinks on “Psych” (9 p.m., USA).