No. (Lateral) magnification is image height divided by object height.


Loosely speaking, the size of an object in the scene as projected by the lens, divided by the actual size of the object, is the magnification. So at 1:1 magnification, a 1 x 1 cm square object will project an image that is 1 x 1 cm on the sensor. It has nothing to do with the size of the sensor--even if the sensor is not big enough to fit the image, the magnification is still the same.


A 1:2 magnification ratio means the projected image has half the size of the actual object.


Note that this definition applies only to objects in the plane of sharpest focus.


It's not necessary to introduce crop factor or any other measurements when discussing magnification--like focal length, it is strictly a property of the lens.


Enlargement ratio, on the other hand, is defined as the size of the displayed image divided by the size of the sensor. So a 24 x 36 cm print (approx 9.5 x 14") taken from a full frame sensor would correspond to an enlargement ratio of exactly 10:1. Contrary to magnification, this is strictly a NON-property of the lens. The two are completely exclusive concepts.


Technical note. Because the real image formed by a typical camera lens is inverted relative to the object, lateral magnification is actually usually a negative number (the image and object heights have opposing signs). But for ease of understanding, the sign is ignored among those who are not optical engineers. However, in certain unusual cases, the sign cannot be ignored because the lens does not invert the image--with rather unexpected consequences.