Depending on the rules in your jurisdiction, it may be possible to have the copy of the passport (or of any other original document) notarized by a notary, attesting that the copy is a true copy of the original. Legally, it may have little meaning, but the stamp and signature on the document will show local authorities that you took extra care and it is amazing how impressed people can be by a rubber stamp.

The usual notary (e.g. at the bank) may not be familiar with how to do this as it requires different wording on the document (the attestation) than is used on the typical notary certification. Find someone who knows what they are doing to do it for you.

Hope this helps.