Not everybody wants to read the scientific papers relating to optics; they are so difficult to digest that even a gearhead can get that numb feeling when trying to really understand just what use they might have in everyday choices about cameras, lenses, and purchase choices. To most avid photograpers the basic practical effects are known and we've all got our way to understand what it means. Since I hate complex mathematics, I've got my own mental short-hand:

1) Almost everything about photography uses the 35mm film camera era as it's reference. The negative size is 24mm X 36mm. When a DSLR sensor is the same size it's called a "Full Frame Sensor". The least expensive full frame DSLR's aren't cheap. A Canon 6D sells for 1,500 EUR (body only) and a Nikon D610 sells for around 1,000 EUR (body only) in France at the time this is written.

2) Most of the DSLR camera sales are for what is generally known as APS-C sensor size, which means a smaller sensor, lower cost, and for a lot of people the smaller overall size and weight of the camera and lenses is much more attractive.

So, full frame sensor DSLR cameras are expensive, heavy and need much more cumbersome, heavy and expensive lenses. And then, a whole lot of people are confused about focal lengths when it comes to comparing the options and what they mean to their own photography. So, back to the 35mm film camera references.

3) A 50mm lens in full-frame is considered a "standard" lens. There's a reason for this. If you close one eye what you see is approximately the same field of view as what you see when you look through a full size sensor reflex camera with a 50mm lens attached. The equivalent in a scope or binoculars would be 1X. (On an APS-C sensor camera a 35mm lens is closest to 1X). Multiples of this are easily understood by just thinking of them as scopes or binoculars. Example, a 300mm telephoto lens is 6 X 50mm, in other words, close to a 6X scope or binocular. A 10X binocular or scope would have a field of view of a 500mm telephoto lens, on a full frame DSLR. It wouldn't be technically accurate, but it would be just as easily understood as a 10 power lens instead of a 500mm lens. (By the way, the field of view with both eyes open is approximately equivalent to a 28mm lens in full frame, which is why street photographers use it so often).

4) As field of view narrows we use the mental short-hand which we call magnification, basically it's a term used to understand the phenomena. What happens when you put a 500mm telephoto lens on a less than full size DSLR sensor is that you "crop" to a smaller field of view. Nikon APS-C sensors are then said to produce 1.5X magnification. All of sudden your 500mm lens becomes the equivalent (in terms of field of view or magnification) of a 750mm lens if you take it off your Nikon D610 and put it on a Nikon D7200.

If you have ever tried to hold "steady" a 10X pair of binoculars, compared to a 7X pair of binoculars, then you know how important "shake" is. It's the same with photographic lenses. That extra reach of the APS-C sensor has a downside: you've got to be even steadier to get a sharp picture. It's magnifying the movement even more.

Remember, we're talking apparent (meaning what you see) movement, not true movement. If you hold your 100mm lens just as steady as your 500m lens, it's not your movement that's changing, it's the magnification of that movement which becomes what's registered on the sensor.

I realize that some of what I've said above isn't pure science, but not everybody is interested in the pure science, only what they might be able to usefully use with the information. It could be of use to the beginner.