100x immersion oil objective acquired
This is a milestone for my reverse engineering work.
I should now be able to resolve details down to about 240nm for green light.

Olympus Plan 100x Oil objective (image is not mine)
The resolution size can be calculated using the following formula and depends on the wavelength of the light and the numerical aperture of the objective.
r = 0.61λ / N.A.
r_b = 0.61⋅450 / 1.25 = 220
r_g = 0.61⋅500 / 1.25 = 244
r_r = 0.61⋅625 / 1.25 = 305
Compared to my 50x objective with a N.A. of 0.60 the resolution is more than doubled.
Some comparisons
Here are some resolution comparison of the same die region (a FC1001) using my different objectives.
Note that my 50x is a long working distance objective, which results in a lower N.A. than if this were not the case.

10x MSPlan 0.30 ∞/-

20x MSPlan 0.46 ∞/-

LWD 50x MSPlan 0.60 ∞/-

100x Plan 1.25 Oil ∞/-
On this specific sample (node size is about 850nm), the 20x objective is enough for reverse engineering, while the 50x facilitates it more.
But for chips with a smaller node size, some details can only be discerned with the 100x oil objective.
Note: the previous images uses focus stacking.
Thin-film interference
Beyond resolution, oil immersion is very useful when working with samples with thin-film interference.
When working at the polysilicon level (metal has been stripped), the die must be coated, otherwise it will be practically unusable.

With some coating, the details are perfectly lisible.

Thin-film interference causing visible artifacts (no coating).

Oil immersion makes the details readable again.