Here's a real-life side-by-side comparison:
I threw some of my stuff on a table, set my D600 up on a tripod, and mounted two lenses on it: My kit 18-105 DX lens set to 50mm, and my kit 24-85 FX lens set to 50mm. I also set the camera to FX mode so it would record the entire sensor when I use the DX lens. These are SOOC images. The only editing done is to resize them for posting here. The EXIF data will be intact so you can check it yourself.
Results:
What the FX camera saw with the FX lens:
What the FX camera saw with the DX lens:
Notice the items are the
exact same size. The only difference is, the DX lens is not designed to cover a full-frame sensor, so it will have the black areas around the edges & corners. The reason for this is a
crop sensor is physically smaller (in this case, 24mmx35.9mm for the full-frame sensor, 23.6mm x 15.6mm for the crop). So a DX-format lens projects subjects onto the sensor the same as it's FX-format focal length big brother..... it just can't cover the entire FX sensor. Had I switched the camera to DX mode for the second shot, it would record exactly the same image as what is shown in the second half of this demonstration:
I repeated the experiment swapping my D600 with my D7000, using the same two lenses. This time, the subjects will 'appear' closer because of the crop sensors' narrower FOV. Both images taken with the same two kit lenses, set at 50mm
What the DX camera saw with the DX lens:
What the DX camera saw with the FX lens:
Granted.... there's a
minor difference in the FOV in all these, but that's simply due to the margin of error. I have no way of knowing
exactly what the focal length of the zoom lens is when I set it. Even though it's
set at 50mm, it may be 48.7mm, or 49.2mm, or 51.6mm.......
The reason the DX images appears to be 'closer' or 'larger' is due to the FOV caused by the smaller sensor. The images are all the same pixel size (800x530), so the DX format appears to make a 50mm into a 75mm. But both 50mm lenses project the subjects onto the sensors at the same size.... the crop sensor is just smaller.