The two-slit experiment was first discussed in the basic section of this tutorial. The basic two slit experiment demonstrates that light is a wave because the banded interference pattern that is characteristic of waves shows up on the photographic plate. The diagram below depicts this.

With advances in technology it is possible to run a more advanced version of the two slit experiment which reveals some of the most shocking characteristics of light. The setup of they advanced two-slit experiment is essentially the same as the basic one. At the end of the experiment their is some sort of a detector plate, such as photographic film. In front of the detector plate is the two-slit apparatus. In front of the two-slit apparatus is a light source. It is the light source in which the two experiments differ. In the basic two slit experiment the light source is essentially a light bulb. The problem with this is that the light bulb is emitting billions of photons per second. It was hypothesized a sting of billions of photons might b able to show wave characteristics, just as water which is made up of billions of atoms can behave as a wave. In order to test this the light bulb was replaced with a light source that emitted only one photon at a time. When the experiment is tested using one photon at a time something very interesting happens.
One photon is emitted from the light source and fired at the two slits. A billionth of a second latter their is a little dot on the detector plate that depicts where the particle has hit it. This at first seems to suggest that light is a particle after all. The experiment is continued and more photons are fired at the target one at a time. After a large number of photons are fired through the experiment, say a million, a familiar pattern emerges. This pattern is the bands interference that indicate waves. This pattern is depicted below.

This is a very interesting trick that the light pulls off. The light is emitted as a particle and it hits the plate as a particle, but light arranges the hits in a shape of a wave pattern. If light is made up of particles, then there should be only two distinct patches of light that represent the two areas behind the two slits. This pattern is depicted below.

So why does the light arrange itself in a wave pattern? This is a question that QMs have been trying to answer for years.
What experiment seems to suggest is that the light leaves the light source as a particle. The photon then speeds towards the target. When the photon gets to the target it goes through both slits and interfere with itself. The interference with itself causes the particles to fall at 'random' into the statistical pattern of interference bands. The photons are said to fall at random into the interference bands because there is no known rule or pattern that governs the motion of the individual photons themselves. The ability of the photon to be in two places at once is an interesting magic trick.
An even more interesting thing about this magic trick is that if it is watched too carefully, it wont work. It breaks down like this. The advanced two-slit experiment is set up just as it is described above, except for one small difference, at the aperture of each slit is put a photon detector. The detector does not obscure the slit, it simply measures for photons and gives off a happy beep when it finds one. If the photons travel through both slits at once, then two beeps should be given off for one photon. When the experiment is run this doesn't happen. A photon leaves the source. It goes through one of the slits causing the corresponding detector to beep and then it smacks into the detector plate. After a million photons are fired through the experiment a pattern is found on the plate. This time, however, the pattern is the one that matches up with particle. It is the pattern of two patches that correspond to the two slits. If the beeps from the detector are matched up with the dots on the detector screen it is found that a beep from the detector correlates with a dot in the patch behind the detector.
These two variations of the two-slit experiment generate some very interesting questions about light. For one, how can a light leave as a particle and then behave like a wave? Another interesting question is: why does the addition of particle detectors at the aperture of the two slits cause light to stay particle? It is these questions and more that QMs have been try to understand for eighty years. Their first solution to this quandary was duality.