Let suppose I have full-frame body and macro lens with magnification 1:1. And I switch to crop body with the same lens. My understanding is because the projection of the lens will be the same, but size of the sensor will differ this will change magnification factor to magnification factor:1
Please explain me if I am right or wrong and why
The magnification will be 1:1, unchanged with that lens at 1:1 on any body.
The only difference is that the cropped body will crop the image.
Say you photograph some 15 mm object at 1:1 with both bodies.
At 1:1, the object will be 15mm on any sensor. The lens does what it does. And that is the meaning of 1:1.
But the full frame will be 36x24mm with a full frame body, and the frame will be around 24x16 mm with an APS crop body.
But within that frame, at 1:1, the 15mm object will be 15 mm on any sensor.
Samples of this at http://www.scantips.com/lights/cropfactor.html
Now we might imagine that the crop body enlarges the object more, because after all, this 15mm object is nearly full frame height in the cropped body, but only less than 2/3 full height of full frame body. But the cropped frame is simply a smaller image (it is cropped), and it must be enlarged more to view it at the same size as the uncropped frame. The cropped body compares to using smaller film in film cameras.
1:1 means actual life size on the sensor. Any sensor, of any size.
The maximum magnification is an expression of the size as it is projected onto the recording medium. That is, it is a reference to the size of the projection on the surface of the sensor or film.
If you have an item that is 20mm long and you're using an APS-C camera with a macro lens capable of 1:1 reproduction, the item will be projected onto the 24x16mm sensor at a size of 20mm. The same lens used on a FF camera will project the same 20mm length onto the 36x24 sensor.
Where the difference will be is when you enlarge the images taken with different sized sensors to the same display size. If you display the images from both sensors at 30x20 cm (12x8 inches), the image from the smaller sensor will be enlarged by a factor of 12.5X while the image from the FF camera will only need to be enlarged by a factor of 8.33X. Thus your 20mm object will be displayed at 250mm in the image from the crop sensor and at 167mm in the image that originated in the FF camera.
On the other hand, if one uses the same enlargement ratio for both images the object will be the same size in both pictures but the total size of the photo from the FF sensor will be larger. If we choose to use the same enlargement ratio of 12.5X for both the APS-C and FF images then we'll wind up with the smaller APS-C image displayed at 30x20 cm but the larger FF image will be displayed at 45x30 cm. The 20mm object that was photographed will be 250 mm in length in both.