Hi Samuel,

There is an excellent article by Dirk Bucher on this:

http://www.bio.brandeis.edu/marderlab/axial%20shift.pdf

If you are a bit uncertain about the thickness of your fructose solution, it is sometimes a good idea to put a small, temporary mark on the surface of the amber to know when you reach that interface.

Good luck.

That article by Dirk Bucher seems very complicated and unnecessary for your purposes (forgive me George).

Instead I will answer your question based on only the PDF you provide. In your PDF they ignore the glass slide cover, perhaps because glass slide covers (refractive index of 1.5) are so close to the refractive medium of the mounting media (and therefore won't really affect the measurement). For the same reason, you do not need to worry about the water/fructose solution (unless you are using a water lens (see below)). The water/fructose solution is also very close to the refractive index of glass and that of the medium the object is in. If you have an extremely precise microscope, this might matter if you also wanted to get an extremely precise measure of thickness. But I suggest that for the vast majority of microscopes, basic instrumental error will cancel out any additional precision you might obtain from factoring in the refractive index of the glass cover and the fluid medium above it.

Therefore, I suggest you only use the Baltic amber index (1.54) as n0, whereas ni will be either 1 or around 1.52, depending on whether you are using either air (dry objective) or an oil immersion lens respectively. If you are using a water immersion lens that is dipped into the water/fructose solution, then you can confidently assert that ni will be 1.49 (the same as your solution). This is going to give you a very similar result to an oil immersion lens (1.52).

The text from the manual is not as clear as it could be. Each interval on the fine focus is 1 micron. They measure a total of 18 intervals (from 9 to 27, i.e. 27 - 9 = 18). Therefore d' = 18 intervals x 1 micron = 18.

no/ni is not below d' (as you suggest). Instead d' is multiplied by no/ni (it is confusing the way they present it). Their example calculation is also confusing because it ignores ni, which is because it has a value of 1 (dry objective), and therefore it has no bearing on the calculation. But it would be better if they included this to make the calculation clearer.

Therefore, no/ni = 1.5/1.0 = 1.5.

And so the total thickness is 27 because d' x no/ni = 18 x (1.5/1.0) = 27.

Basically, unless you use a dry objective, your actual thickness (d) is likely to be more or less the same as your stage movement (d'). This is because ≈1.5/≈1.5 (no/ni) = ≈1. And so d = d' x ≈1 = ≈d'.

I hope this helps. Please reach out if you are still confused. I am also learning this stuff for the first time (I could be wrong about some of the above and let me know if you think so). Thanks for this interesting question.