DX vs FX the final comparison

Question

There are a lot of questions about using specific lenses from one format to the other, but I was hoping for a comprehensive overview of all combinations that is easily referenced. For the sake of math, lets choose a '100mm' lens. I know that that DX cameras, for example have a 1.5x drop factor, so a 100mm DX lens actually looks like 150mm on a DX camera. I have also heard that using a DX lens on an FX camera reduces the megapixels since it is only using part of the sensor. Etc. So, again for easy math and the sake of of having a good reference-able comparison.

If you have a '100mm' DX lens what happens when you:
Use it on a DX camera.
Use it on an FX camera.

If you have a '100mm' FX lens what happens when you:
Use it on a DX camera.
Use it on an FX camera.

Answer 1

Be careful here. A lens does not know what camera it is mounted to. Its popular folklore that a lens "acts longer" on crop sensor camera (Nikon DX, Canon EF-S). This is technically incorrect. The proper term is "crop sensor" and what the image looks like is exactly the same as if you took it on a full frame camera and cropped it. Exactly.

Take as an example, a DX/EF-S lens. Mount it on a crop sensor camera on a tripod. Take a photo and then swap to a full frame camera at the same place, looking at the same scene. Take a photo. Now mount the same lens on a view camera (most are at least 4x5) and take the photo. In all cases, the lens is the same, it did not magically grow by 50%. In fact, the good image will be exactly the same size on each of the three cameras.

There is no difference in the relative compression that a long lens shows, etc.

It is more accurate to think that shots taken on a crop sensor camera are pre-cropped.

Answer 2

Things get much easier if you forget about millimetres and focal lengths and talk about angular field of view.

If you have a '100mm' DX lens what happens when you:

Use it on a DX camera.

You get a horizontal field of view of 13.5 degrees (corresponding to 150mm on a full frame sensor)

Use it on an FX camera.

You get strong vignetting, or your camera crops the image reducing the resolution to 44% of the pixels leaving you with a horizontal field of view of 13.5 degrees (corresponding to 150mm on a full frame sensor)

If you have a '100mm' FX lens what happens when you:

Use it on a DX camera.

You get a horizontal field of view of 13.5 degrees (corresponding to 150mm on a full frame sensor)

Use it on an FX camera.

You get a horizontal field of view of 20.4 degrees (corresponding to 100mm on a full frame sensor)

Here's the same information in a handy table:

 +---------------------------------------------------+
 |          |    FX sensor       |      DX sensor    |
 +---------------------------------------------------+
 | FX lens  |  100mm equiv fov   |  150mm equiv fov  |
 | DX lens  |  150mm equiv fov*  |  150mm equiv fov  |
 +---------------------------------------------------+

*when used in crop mode, otherwise the lens will vignette a certain amount and the usable field of view will depend on the particular lens, zoom setting, aperture and focus distance.

Answer 3

You can compare the behaviour of DX and FX lens on various DX and FX bodies graphically with the nikkor lens simulator.
You can experiment the field of view, % of crop and more with lens of various focal length on DX and FX bodies.