Images on personal computers - Which aspect of size to keep constant?
I don't think that (2) works. The physical size of the screen is not available to you. You may be able to calculate the dimensions in pixels, but pixel density (dpi), pixel format and sampling pattern change from screen to screen. So you won't be able to calculate the centimeters from the pixels.

I would do what web designers have done for centuries: rely on the user to resize content to their needs.

I would provide images in high resolution, display them at an initial size* that works well on the most common screen resolutions (1366 x 768 and 1024 x 768), and provide a highly visible request to resize the image to make viewing comfortable. With Javascript you can offer fluid, continuous resizing options easily (e.g. TwinHelix or, what I prefer, YUI), allowing the users to resize web content in the same way they would resize the browser window. Or you can offer a number of preset sizes (+/- 10% etc.) and link these to different style sheets.

*A good measure for the initial size, in my opinion, is the em. You can rely on two factors with this: if the user uses the computer at its factory settings, then type size is adapted to the screen size; if the user changed the settings, then type size is adapted to his visual ability and preferences. If you give image size in em, i.e. in relation to type size, images will be scaled to the users needs.

This is, of course, no exact science, but that is what I do, when I design a website. It is the closest I manage to get to cross computer similarity in size. As soon as you read about cross browser web design, you'll lose all optimism that your goals at exactness can be achieved ;-)