A few questions on Nanotechnology (Microscopes/Optics)

I've been going through some past papers in preparation for my exam tomorrow. We have not been given the past paper answers so i was wondering if anyone could help me with some of the answers. I will post multiple questions here but help with any of them would be greatly apprechiated

Homework Statement
A microscope equipped with an oil filled objective lens with a numerical aperture of 1.2 is used to
image the patterned features on a semiconductor substrate. Define what is meant by the numerical
aperture and explain why the lens is oil filled. Using the Rayleigh Criteria, define the smallest
resolvable features when light of wavelength 633 nm is used to illuminate the substrate and the oil
filled objective is use

The attempt at a solution
Numerical Aperture is a numerical value which indicates the range of angles at which a system can accept/emit light

I know d = (0.61[Lambda]) / 2nsinu
and NA is nsinu.

Therefore d = (0.61*633*10^-9)/2.4

Is this correct? and why is the lens oil filled?

Homework Statement

A tube scanner made of a PZT piezoceramic material, which has a piezoelectric coefficient, d31=-
0.27x10
-9
mV
-1
, has a length of 12.5 mm and wall thickness of 0.5 mm. Calculate the ratio of
displacement dz per unit volt. How could elevated temperatures affect the piezoceramic material?

The attempt at a solution

Using a formula i can show that dz/U = L / h d(31) = 12.5*10^-3 / 0.27*10-12 * 0.5*10^-3

Is that correct for the displacement dz per unit volt, and how does elevated temperatures effect the materiel?