Is there a way to measure the thickness of a metallic plate of order of micrometers? I have a $5 cm×5 cm×? \mu m$ copper plate.
Where '$?$', the thickness of the plate, is really small (about 30um).
Is there anyway using physics to calculate the thickness?
Update:

Sorry I forgot to say that the plate is attached to a non-metallic plate which is bigger than the copper plate from beneath.
For instance: its a Printed circuit board.
 A: Do you have access to a precision balance? Then you could weigh the plate, and using the known dimensions of the plate and the density of copper, compute the thickness. For $5\,{\rm cm} \times 5\,{\rm cm} \times 30\,\mu{\rm m}$ the weight would be $0.672\,{\rm g}$ for example. The precision of that measurement depends on how accurately you can measure the dimensions, and if the copper is pure or an alloy.
Or you could use a simple micrometer screw gauge.
Edit: As you amended that the copper layer is attached to something, these methods won't work as they are. They would both work if you knew the properties of the thing the copper is attached to. If you have multiple samples and it is possible to destroy one, you could etch away the copper (assuming you can selectively etch the copper, but not the other stuff), and then measure either the weight or the thickness of both the boards with and without the copper and substract them.
A: I calculate that with 30u thickness we have 675mg mass. Use a microbalance and weight the sample.
A: If you are reasonably confident about the quality of the plate in question (uniform thickness, a well-defined square shape, etc.) you can measure the resistance of the copper square. This would be a non-destructive method for the arrangement in the OP.
The specific resistivity of copper is (per google search) $1.68 \div 1.72 \times (10^{-8} \Omega\,m)$ (depending if it's annealed or not). Let's take 1.7. Since this is a square piece of copper, only the thickness is relevant.
$$R = \rho / d = 1.7 \times 10^{-2} / d_\mu $$
where $d_\mu$ is the thickness in micrometers and $R$ is in Ohms ($\Omega$). For a $30\,\mathrm{\mu m}$ piece the resistance would be 0.567 milliohms. Small, but quite measurable.
