I would say this is most likely happening because either:
- the software you are using to print the image is scaling it down prior to sending it to the printer
- the selected printer driver settings are set to scale down the image before printing
If I were to guess, I'd say it was the first option.
Digital images are made of pixels, which don't have a fixed conversion to real world units of length. When you say that the
.tiff file is 3.5cm what this will mean is that the file has information stored in its metadata that defines it's resolution per inch/cm such that it would print at that size, if the printing application takes said information into account.
Your likely issue is that some programs may default to resizing an image, say if it's too big to fit on the page area that a printer can handle.
For example, if I open an 'A4'
.tiff file (2480x3508pixels at 300ppi) in GIMP and hit print, it'll print out slightly smaller than A4. My printer can't print right to the edge of the paper, so GIMP scales down the image so it'll all fit (overriding the 300ppi setting in the images metadata).
Recommend you check the print settings in the application you're using to print the image and look for an option like
scale (should be 100%) or
hight values and check they're what you're expecting.
If you can't find a solution to your issue there (or anything in your printer preferences about
Reduce/Enlarge Document or similar), then provide more information about exactly what software you're using to print the image, and someone familiar with it may be able to provide specific instructions.