Question on matrilineally in Orthodox Judaism.

Hello everyone! I’m not a Jew but had a question regarding how Jewishness is passed down within the Orthodox section of Judaism. It’s my understand that Jewishness is passed down through the mother. So if your father was a non-Jew but your mother Jewish, then you would be a Jew, but is the child considered as Jewish as his/her mother or less because of the non-Jewish father? If they are considered as Jewish as their mother, then hypothetically if the daughter of the Jewish mother had a child, would they be classed as as Jewish as their grandmother? Where does this line of Jewishness end if it even can? Sorry for my ignorance or stupidness if it comes across as that! Thanks!