# Focussing a laser beam through a sapphire substrate

I am in the middle of focusing a blue (400nm) laser beam through a sapphire substrate, of thickness 430 microns. To do this, I am using a LD-Plan Neofluar 63x objective lens, which is equipped with a coverslip correction collar.

If this were glass, I would merely adjust the coverslip correction to 430 microns, and the thickness would be compensated for.

However, how should I adjust the correction for a substrate of different refractive index? (Assuming for simplicity sapphire is optically isotropic)

Is there any equation which allows you to find the optimum correction for such a system?

I have tried using a correction of 430 microns, and the optical spot was outside the sample completely. In contrast, a correction of 170 microns (which I tried first by mistake) gives a relatively good focus, so the change in refractive index is obviously very important!

Many thanks in advance!

Well, what is the index for sapphire? ... http://refractiveindex.info/?shelf=main&book=Al2O3&page=Malitson says it's 1.7866 at 400 nm. BK-7 glass is 1.53, so if the correction collar were linear, you'd adjust the correction by at $\frac{1.7866}{1.53}$ .