Full Frame (FX), Crop sensor (DX) Confusion?

Hi, I'm really confused on this. I know that the Crop sensor (DX because i use nikon) or APS-C i think it's called has a smaller sensor than a full frame. My understanding is that when you put an FX lens on a DX its focal length is multiplied by 1.5 (Am i right?), but when you put DX lens on an FX the image is cropped. When they say it gets cropped does it mean it actually creates a smaller image? So if a Full frame camera normally produced a 6000x4000 image would it be 4000x2666 or something with a DX lens on it? Please correct me on this if i'm wrong.

So if an FX lens on a DX body is multiplied by 1.5 for focal length, would it produce the same quality? For example if i put an FX lens on a DX body with a multiplied focal length to create a focal length of 400, would a DX lens with a focal length of 400 be better quality? (Not including the quality differences in the lenses themselves!)

So to summarize if you put FX lens on DX body the focal length would be multiplied by 1.5 right? And if you put a DX lens on a FX body it would be a smaller image correct?

You're probably talking about Nikon (the Pentax K-1 isn't out yet, but adjusts the same way, and I'm not sure about Sony, but suspect as much).

A 400mm lens is a 400mm lens, it has the 35mm equivalent of a 600mm on cropped-sensor cameras, but that's about it.

If you put a lens designed for a cropped-sensor Nikon on a full-frame one, part of the sensor is blanked off automatically, so you're effectively using a smaller sensor. If you mount a cropped-sensor Canon lens on a full-frame body, you're shelling out for Canon to replace the broken reflex mirror - I strongly advise you not to try it.

Any lens made for an FX body will give give you an image on a DX body that is is 1.5 times the focal length because of the sensor being smaller. Imagine a 9" x 5.33" image cut from the center of a 12" x 8" image that was taken on an FX body.

So if you use a DX lens on an FX body, the camera will switch itself to DX mode and only use the center of the image sensor for the DX lens. You math seems to be correct. As far as quality, the resolution will change, but not the quality of the optics.

Here is a link that may end your confusion.

When you use an FX lens on a DX sensored camera, the angle of view is narrowed due to the size of the sensor, but the lenses focal length stays the same

Focal length NEVER changes!

Let's just get that clear. 35mm on FX is 35mm on DX. What the 35mm sees on FX though is 1.5X wider than in DX. That's what's different - the angle of view. That' why they just mention it as equivalent. The 35mm on a DX is equivalent to a 50mm on FX.

You are correct saying that the DX lens will project a smaller image on the FX body and some selected full-frame bodies automatically crop the saved image to delete the ugly fuzzy borders when a DX lens is attached to them but overall, you shouldn't do this since normally the DX lens might damage the reflex mirror of the FX camera.