In photography, ISO is a term used to refer to the function that controls the camera's sensitivity to light. Or simply how sensitive the camera is to light; a high ISO translates to a brighter image than a low ISO. The origin of the name comes from an organization that is in charge of global standards for measurement. When making film for cameras, film makers would have to make their different models in compliance with the International Organization for Standardization, and so they would refer to different stocks as their compliance number, or ISO for short. The organization has three official languages: English, French, and Russian. Originally, the organization's logo in two of its official languages, French and English, are abbreviated to OSI or ISO depending on English or French. Due to the difference of terms in different languages, the organization decided to choose ISO as the official term due to the greek word "isos" which means equal. So basically, the function on a camera called ISO is not an abbreviation for the action that it performs, but rather the organization that was influential to its creation and application.
Now, to get to how to use it when you take photos. Its outcome is the same regardless of digital or film, but application is very different. In theory, ISO 200 on a digital camera would result in the same exposure as ISO 200 on film. However, with film, each roll is fixed to a specific ISO. With digital, changing the ISO doesn't literally change how much light the camera's sensor detects, but rather changes it's parameters of how much light to use. The "normal" ISO range on a digital camera is about 200 to 1600, but with more recent increases and more money spent, you could get cameras that go as low as ISO 50 and even as high as ISO 3 million which is absurdly high.
When you increase your ISO, in both film and digital applications, you are subjecting yourself to something called 'noise.' Noise looks like grain, or sand covering your image. With higher ISO, more noise appears. In digital, the noise looks like a bunch of small red, green, and blue dots scattered across your photo. In film, the noise looks a bit less intrusive, but still takes away from overall clarity and detail in the image. Another thing about film ISO is that not all rolls (or stocks) of film are different. Even two different stocks from the same brand will not look identical because of slight differences in chemicals during each batch of film created. Of course if you buy 2 rolls of the same film, you are going to get a very similar look, but if you focus one very exact and specific details in the dark room, you will be able to spot differences in the rolls. In the same way, all different models of digital cameras will have different limitations and grain addition for increasing the ISO value. On my older camera, I would see about the same amount of grain at ISO 1600 that I do when shooting at around ISO 2800 on my newer camera. And as newer and more advanced cameras come out, the maximum ISO level will continue to be pushed so that more versatile and incredible cameras are produced.
Here are some examples of what noise looks like in different photos.


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