The camera obscura (Latin for a darkened room) is an optical device that projects an image of its surroundings on to a screen and was one of the inventions that led to photography. Consisting of a box or room with a hole in one side, light from an external scene passes through the hole and strikes a surface inside where it is reproduced, upside-down, but with colour and perspective preserved.

To come across Anish Kapoor's startlingly beautiful C-Curve sculpture in the middle of Kensington Gardens is to experience the effects of the camera obscura but without the darkened room. Walk towards the highly polished concave surface of stainless steel and the surrounding lawns, autumn trees and people will appear upside down like a child's vision of Australia, where everything is topsy-turvy. Move around to the bulging convex facade and the world will be the right way up again.

Clouds, dog-walkers, babies and bikers all pass across the silver screen in a filmic version of real life. The players in this pageant stroll on and off stage passing, only for a moment, like the shadows in Plato's cave. "Life's but a walking shadow, a poor player, That struts and frets his hour upon the stage, And then is heard no more," Macbeth despaired. What is real? What is a chimera? asks Kapoor in these mirroring multiplications and inversions of our surroundings, which pose questions about our very existence.

From the first encounter with these four stainless steel structures placed within Kensington Gardens, we are reminded that the world is rarely what it seems. As Alice discovered in the looking glass, reality is a slippery concept. The symbolism of the mirror is ancient; from Narcissus to Snow White, it is an image that has caught the human imagination.

Legend has it that in 212 BC Archimedes repelled the Roman fleet, laying siege to the island of Syracuse by using a multitude of flat mirrors that acted like a huge concave mirror to direct the sun's rays to burn the attacking Roman fleet. In the 17th century, Newton realised that mirrors rather than lenses could solve a problem called chromatic aberration. By using curved mirrors in telescopes the integrity of light could be maintained rather than defracted. For 2,000 years geometry had been flat but by the 19th century mathematicians had overturned Euclid's thesis that the angles of triangles had to add up to 180 degree and that parallel lines did not meet. Kapoor's curved reflective surfaces reveal the universe as it really is, a place where light warps and bends and things are not what they seem.

Sitting in the Round Pond in front of Kensington Palace is a polished red dish like a vast setting sun, which reflects the movement of the clouds above. As with the human mind, images float across its surface, staying a while and then drifting away. Though Kapoor is, presumably, not responsible for the swans that swim around it, he must have been aware how their white forms sailing past are a perfect visual complement to his primary red.

The placing of Kapoor's sculptures in the park is critical. The long vista leading down to Kensington Palace accentuates the sense of infinity within the works' reflected surfaces. Elsewhere Non-Object (Spire), a reversed trumpet shape that echoes his Tate Marsyas, sits among the trees, its silver skin covered with rain drops: part religious icon and part futuristic form. As you walk towards it a second spire is reflected in the base of the larger. When you arrive up close it disappears like a mirage in an oasis. So much of Kapoor's work is dependent on the involvement of the viewer.

Walk across to The Longwater and there you will come across another Sky Mirror, a vast sphere standing like some huge satellite dish where a Henry Moore sculpture once stood. On a grey day it looks inert but when the light plays across its surface, boundaries between sky, reflection, reality and dream are blurred.

From his early pigment sculptures that constructed deep voids, Kapoor has asked questions about the nature of existence and belief. He investigates what we hardly know, turning the world upside down and inside out to extract meaning. It gives us a glimpse at the mysteries both of the human imagination and the universe we inhabit.

Until March 2011