Christen Købke: Great Dane

The 'o' has a slash through it. You say the name like "Kirbke". But so far, the name itself hasn't been much used by English-speaking art folk. If you know his work, it's possibly a picture in the National Gallery already, with its surprisingly deep red wooden drawbridge. But now you can see much more of him there. Christen Købke: Danish Master of Light opens today.

There's something to be said for him. Yes, he's one of those rediscoveries. And what's the best way to make the introduction? Do you want to hear about context, about Denmark's Golden Age, Hans Christian Andersen, Søren Kierkegaard, and wonderful – or was it so wonderful – Copenhagen? It seems to me that a few simple facts are what we need.

Købke's life was short: 1810-48. He died of pneumonia. To judge from the work in this show, his really creative period was very brief and very precocious. It happened in his earliest twenties, before he left his homeland and travelled to Italy.

His father was a master baker, employed by the army, and the family lived in "The Citadel", the fort outside the capital, a brick structure with towers and pinnacles, a place that offered much of his subject matter. His art teacher Christoffer Wilhelm Eckersberg recommended the pursuit of the ideal through the real. There is nothing to suggest that Købke saw the artistic life as an act of rebellion.

Quite the opposite. You might call his work an art of obedience. He practised an exquisitely heightened realism. What he looks at is everyday, prosaic – buildings, skies in fine weather, people standing around, steady faces. There's no hint of symbolism or ghostliness, nor anything shockingly frank. But there is a hypnotic quality in Købke's gaze. The intensity is in the level of his attention.

The paint, the light, is clean, clear, sharp, minute, precise. Nothing, absolutely nothing, is fudged or overlooked. Everywhere you scan, the artist has got there first. Everything is given an equal treatment, an equal focus. And everything is rendered at such extreme close-up that it may elude normal eyesight. The approach is miniaturist, both microscopic and telescopic. There is an almost cellular observation of the skin of a face, and an eagle eye that can grasp every distant detail of brickwork or bark. The picture is ahead of you. You can go on going into it, and it will out-explore you.

To take the most outrageous example. Roof Ridge of Frederiksborg Castle, with View of Lake, Town and Forest is a kind of landscape, with a high vantage point. (One of Købke's tricks is the non-standard view.) There's the roof, a dark, straight strip, and viewed above this there's a strip of landscape, stopping at a horizon at about two-fifths up. The rest of the square picture is occupied by a totally empty pale blue sky. And the outrage is that even this area is treated with miniaturism. There is this apparently uniform field, but there is no filling-in. Each minutely variable speck of blue is registered. You can look at every bit of it.

At the same time, and this is equally miraculous, Købke's miniaturism is exactly balanced. The details, so clear, never become bits that stick out from the ensemble. Stand back from the painting, and the minutiae – the creases of crow's feet, the tiniest ripples on a lake surface – resolve into a photographic sight. Købke is one of those painters who worked just on the cusp of the invention of the camera, around 1839, and who seem strangely to have foreseen its chemical truth. His light and shade are pitch perfect.

Take another breath-taker. In Frederiksborg Castle in the Evening Light, the deep red castle is reflected almost fully in the moat beneath it. It's amazing how he judges the modification between real building and its water-image: very slightly darkened, very slightly blurred. Reproduce these pictures in black-and-white, and the accuracy of their tone would be astonishing.

You would miss something vital, though. Combined with Købke's intensity of attention, there is a contrary heightening. What he does with colour is a kind of fiction. A scene is mapped out into units of colour. The colours may be subfusc, but they're concentrated. In a portrait, like the Old Sailor, each item of clothing has its dominant colour brought out, even if it's a dull dark blue grey, or a dull brown green, and the flesh glows with an inner orange. You couldn't call it visionariness. But this colourising is what gives his art a delicate transfiguration.

There are also some very surprising compositions, usually done as one-offs. Look at The Cigar Seller at the Northern Exit from the Citadel. Is it a scene of passing everyday life, or is it a sitting portrait? A path, a tree trunk, a lake in the distance, a group of men and child over there – but at the front the tradesman sits at his stall and turns his face to the viewer. He suddenly breaks out of the scene, introducing an unexpected intimacy.

Or there's One of the Small Towers on Frederiksborg Castle. It ascends through the picture space, its pinnacle going through ever-more-narrow stages, until finally it arrives at a fine upright point, which very nearly but not quite pricks the top edge. It could be a metaphor for the precision of Købke's fine handiwork. Sadly, seen by a ceiling of artificial light, the effect will be lost. A strip of shadow will be cast across it by the frame. Pictures like this need daylight.

Or take the View from Dosseringen near the Sortedam Lake Looking towards Norrebro (I'm not sure who devised the titles, but they want to assure us that nothing was made up). Two women stand, backs turned on a jetty. A row boat with a full crew is just far enough out on the water to make its intentions obscure – coming, going? A Danish flag stands dead centre like a sentinel. This painting is the nearest that Købke gets to Caspar David Friedrich's mystery and spirituality. Or put that another way: if you find Friedrich a bit over the top, this is the tactful, sensible version.

And Købke is always tactful, sensible. Whatever his accomplishment, you meet his limits. He's an artist who know his restrictions and keeps to them. He works with sincerity, modestly, with commitment. What he does, he does extraordinarily, and invariably successfully. But what drives him is not inspiration; rather, a sense of duty. His self and self-expression count for nothing. His hand carries a great responsibility. He must get it absolutely right. If he weren't infinitely careful, if he made the slightest slip, he would break his word to the world.

There is something amazing and admirable and attractive about this vision. But it isn't the kind of painting that will shake you. Its discipline is not a case of wildness being tensely tamed. His work is never on the edge of violence or vulgarity. There isn't that pressure in it. And I'm afraid that care and consideration, however dedicated, are not going to be enough. What we want from art is not the same thing that we want from the people next door.

Christen Købke: Danish Master of Light, National Gallery, London WC2 (020 7747 2885) today to 13 June; then at National Gallery of Scotland, Edinburgh (0131 624 6200) 4 July to 3 October