Tacita Dean, Turbine Hall, Tate Modern, London

Tacita Dean takes on the vast space of Tate Modern's Turbine Hall and triumphs in magnificent, amusing style

The recipients of a Unilever Series commission must open their letters of invitation with mixed feelings: elation at having officially hit the jackpot, foreboding that they are going to have to make something.

It's not just that the Turbine Hall at Tate Modern is the most visible site in contemporary art. It is that it is very, very big.

The Tate's foyer is 115 feet high and more than three times as long. That is all very well if you are, say, Anish Kapoor, whose Marsyas turned it into a 500-ft plastic vagina. It needn't trouble you unduly if, like Olafur Eliasson, you make vast installational micro-climates or, like Bruce Nauman, your art consists of sound in space. But what if your medium, the one you love most, is just 1.377 inches wide?

That was the problem facing Tacita Dean, whose Unilever commission, tellingly called FILM, opened in the Turbine Hall last week. Dean is a wonderful artist, as was confirmed by her failure to win the Turner Prize in 1998. Her work is clever, poised and allusive: it was never going to do well in a shouting match. She is best known (and best at) making films, the power of these lying in their apparently haphazard subjects – an empty house, the view from a revolving restaurant, a boat, birds in a tree. What matters as much as what these films see is how they look, Dean favouring the deep saturations and historical resonance of 35mm (or 1.377 inch) film stock.

Thus her problem with the Turbine Hall. Dean has described herself as needing "the stuff of film as a painter needs the stuff of paint". Her relationship with the medium is visceral: the death of analogue film at the hands of digital is a source of real mourning to her. And so FILM is both a triumph and a failure, or rather a triumph that concerns itself with failure. Dean's Unilever work is a species of last rites, read over the deathbed of something inconsiderable. And it is read in the vastness of the Turbine Hall. Eliasson gave us the Sun, Carsten Höller, helter-skelters, Ai Weiwei, 100,000,000 sunflower seeds. One fears for Dean's success.

But unnecessarily. As you look at FILM, something strikes you as wrong. Several somethings, in fact. Dean's installation is just what it says it is, a 35mm movie projected on to a screen halfway down the far end of the Turbine Hall. It is a moving picture, and yet it is also a still: the sprocket-holes of celluloid film stock appear as a static frame down the image's sides. Worrying, too, is that from time to time in FILM's 11-minute loop, the screen on which it is projected seems to turn transparent, so that we are looking through it at the Turbine Hall's east wall. Last, FILM is the wrong way up. Movies are made in landscape format, wider than they are high. Dean's is tall and thin, which is to say in portrait format. Which is fair enough, because FILM is a portrait of film.

And what a portrait. Somewhere in the ponderous phrase "lens-based art" is a whiff of impropriety, an assumption that lenses and art-making are mutually exclusive things. Bollocks to that, says Dean, who squares up to modern art on its own home turf and takes on all comers.

For a few seconds, FILM is a Mondrian – the Dutchman was a great fan of Walt Disney – the modernist grid painted on to Dean's celluloid by her own hand. A moment later, a large yellow disc is superimposed on the Turbine Hall's end wall, just where Olafur Eliasson's large yellow sun once hung. The Paramount Pictures trademark mountain, up-ended and doubled, becomes a Gilbert & George turd; the escalator from Mark Wallinger's Angel runs the right way. If FILM had a soundtrack, it would be "Anything you can do, I can do better". Dean's film ponders art, giggles, thumbs its nose, scampers on. It is, among many other things, very funny.

If you're looking for gloom in her Turbine Hall installation, in other words, then you are going to be disappointed. FILM is, perhaps, not so much a eulogy as a meditation on immortality. Celluloid may be doomed, but it is a happy doom, and a beautiful one. The tricks of cinema and the tricks of painting are both to do with illusion, making us see things that are not there. Thanks to Dean, those skills survive. This is a magnificent work, one whose passion dwarfs the Turbine Hall, the massive ego that is Tate Modern. See it.

To 11 Mar (020-7887 8888)

Next Week:

Charles Darwent heads north for the Turner Prize at Baltic in Newcastle