The Mystery of Crop Size

The DX sensor chip that actually records the light coming through the lens in your camera has a smaller area than an FX (full-frame) chip. They use the FF chips in D3, D3x and D700 cameras.

Your lens projects a given-angle cone of light from its rear, depending on the focal length and subject and sensor distances from the optical center of the lens in its current state, the optical design and masking of the back of the lens. DX lenses like your 18-200mm lens, because of the last two factors, do not completely illuminate a full 24x36mm frame -- so they can be used on FF if they will mount (which they should if they are 'F' mount), but they may just light a circle in the center of the frame.

FX or film compatible lenses, OTOH, project a larger circle of good illumination that entirely covers the frame with an evenly lit and focused image (theoretically, if used properly). If you use a FF lens on a DX camera, the smaller sensor will only record a portion of the entire projected image, in the center of the circle. The lens does NOT change it's focal length -- everything about what it shows is the same no matter which camera it is used on: focal length, depth of field, quality and quantity of illumination, size of projected image, etc. (The DoF effectively changes based on the proximity and size of sensor elements, but that's another discussion.)

Crop factor is a relationship of a DX sensor to an FX sensor, for this discussion. If you have a crop factor of 1.5x to apply to your lens / camera system, then the image the sensor records is being compared to focal length required when used on a FF camera to produce the same image (or image magnification) at a given distance. To keep the subject the same percentage of the frame size on different sensors at the same distance from the subject, you would have to use a 1.5 time longer focal length on FX as on DX.

/..