In school, we all learned that from white light we can only perceive the visible spectrum but we can't see UV or the IR portions.
If this is the case, then how come we can do infrared photography?. OK fine, the lens can do it but how can we see the IR colors in the final picture? How do we really know that it is the IR light and not just dramatic colors?
"Colour" is essentially a property of the distribution of wavelengths of visible light (as perceived by humans).
Digital cameras only detect the amount of light at each pixel, they can't measure the wavelength and thus can't record colours directly. Colour images are produced by placing alternating red/green/blue filters in front of each pixel. By placing a red filter (one that blocks green and blue light) in front of a pixel you can thus measure the amount of red light at that location.
Infra-red photography with standard digital cameras involves filtering out visible light (and optionally removing the built in IR filtering) so only infra-red light is recorded. The alternating red/green/blue filters remain in place.
There are different wavelengths of infra-red light, however these wavelengths don't correspond to "colour" because they are invisible to the human eye. True infrared, in the 850nm and longer range passes more or less equally through each of the red/green/blue filters so you end up with an intensity only (greyscale) image, like this:
http://www.mattgrum.com/photo_se/IR_1.jpg
Wavelengths that are closer to the visible spectrum, so call near IR in the 665nm range will pass through the RGB filters in different amounts so an image with different RGB values is produced and hence when displayed on computer you get a colour image.
But the colours aren't "real", in the sense that colour is an property of human vision and these wavelengths are outside our vision so the brain hasn't defined a way of presenting them to us. The different colours you see in a digital infrared image (reproduced in the visible range by your computer monitor) arise due to a deficiency in the blue and green filters.
The blue filters are designed to filter out the lower frequency red and green light, but around the visible spectrum range (as the camera's IR filter normally takes out everything else). When visible light is blocked and frequencies get really low (like those reflected by foliage via the Wood Effect) they start to pass through the blue and green filters again!
So the very bottom of the visible spectrum/very near IR (which is plentiful in the sky) mainly excites the red pixels as the blue and green filters are still doing their job, near IR (reflected from leaves) starts to excite blue and green pixels as the filters are operating outside their normal range.
The result is a red looking sky and blue/turquoise looking trees, like this:
(source: wearejuno.com)
But since these colours aren't reall real, photographers often swap the red/blue channels around, which gives more normal looking blue skies and green/yellow trees:
The image we can see from an infrared camera is what is known as a false color image. What this means is that a range of wavelengths in the infrared spectrum are rendered with a corresponding wavelength of visible light. Just as with visible light, a particular wavelength of infrared light can vary in intensity from just above black (shadows) to near saturation (highlights).
How each wavelength and intensity of the infrared light is translated into the visible light we can see depends a lot on the purpose and intended usage of the infrared image. It also depends on whether the image was captured with a camera designed from the ground up to record light in the infrared spectrum or with a camera designed to capture visible light that has been converted to capture infrared light by removing the infrared filter found on most cameras and adding a filter to remove visible light.
Images from astronomical instruments that photograph the night sky in infrared tend to be processed so that they look like the visible night sky even though what is visible in the heavens and what is not will be different in an infrared image than what is visible in a visible light image. Typically, shorter wavelengths of infrared light will be rendered as shorter wavelengths of visible light (blue), medium wavelengths of infrared light will be rendered as medium wavelengths of visible light (green), and longer wavelengths in the infrared spectrum will be rendered as longer wavelengths in the visible light spectrum (red).
On the other hand, images used to see humans in the dark ("night vision" images) will often display different intensities of the same wavelength (10µm - the wavelength at which humans radiate the most heat) using different colors. In that case white might denote the highest intensity at 10µm, red might denote a slightly lower intensity at 10µm, green an even lower intensity, and so on. The other wavelengths of infrared light might not be rendered at all.
Examples of each of the above scenarios are visible near the top of the Wikipedia article on Infrared.
Yes, infrared photography does record infrared wavelengths. Usually, a filter is used to make sure no visible light gets recorded. Sensors and films are not based on human eye, so their limitations are different. We can see the infrared light on resulting photographs because it is displayed in some other color(s) than infrared.
In photography, colors in resulting photograph are rarely an exact match with original view; in fact, it takes great effort to keep colors from changing throughout workflow. There are several techniques taking advantage of mutating colors more or less, such as cross-processing, HDR, black-and-white etc; and IR photography is just one of them. X-ray imaging is another example of turning invisible wavelengths into visible ones.
The camera is a grid of sensors which count photons from a given range. They count these photons, and produce a table showing the frequency of photons (how many photons per unit time, not their EM frequency) for every sensor on the grid.
In practice, cameras have sensors optimized for catching red, blue and green photons, but they so happen to also catch infrared. Using filters, you can allow only IR onto the sensors. You will then get a table of numbers showing the frequency of photons in the IR range.
You are now free to do whatever you like with this table. You can plot it as a 3D function with the frequency as height. You can map low numbers to black and high numbers to white, to produce a grayscale image. You can map low numbers to black, medium numbers to orange-yellow and high numbers to mimic the way red-hot metal glows.
The reason you can see the IR colors is because the camera doesn't produce an image with exactly the same (IR) colors that it saw. It produces a transformed image, where every IR wavelength is mapped to a visible wavelength. This isn't done by software, but it happens by itself: The sensors normally catch both visible and IR, but the software assumes it's all visible because there is an IR filter blocking photons with IR wavelengths. But some people remove the filters.
It's all possible to make special thermal cameras, where the sensors are actually optimized to catch IR. These would probably have software explicitly converting IR to visible light.
