You don't really need to worry about the refractive index for zeta potential. But it is a mandatory information when it comes to DLS. For silver, the RI is 0.135. :)
The optical properties are not required for DLS if the robust intensity distribution is used (most robust parameters are the z-average and polydispersity index, PDI). They would only be required if an attempt to convert to a volume distribution was made. The conversion to number should never be attempted
There are 2 parts to the RI - the real part and the imaginary (absorptive) part: RI = n - i.k
The values of both n and k are wavelength dependent. The most commonly used laser in DLS is the He-Ne at 0.6328 microns
The optical properties of silver and many other materials can be found in databases such as: https://refractiveindex.info/?shelf=main&book=Ag&page=Johnson where primary source material is quoted
According to the above site (screen dump attached), the RI values for silver at 632.8 nm are: RI = 0.056 - i.4.28
Quotation of an RI without a wavelength is practically meaningless especially for metals where the parameters can vary considerably. Couple of points:
There are 2 parts to the RI - the real and imaginary parts. A real part of ~ 0.15 is seen at 340 nm. See attached
On the surface (5 - 10 atomic layers) of material, silver is fully oxidized when in air or oxygen containing liquids (e.g. water). That is in the +1 oxidation state and not silver metal, Ag0. More information in the webinar noted above. Nanoparticles have considerable surface exposed to the environment
The RI properties of the particle are not required for zeta potential/mobility determination or for the intensity distribution in DLS