Jews are a religiuos group and an ethnicity, but not a race. So there is no Jewish physical look. Since Jews are mostly Semitic, there maybe some physical features which are common to many Jews. Jews may be also recognisable because of their look when they wear beards. But many Gentiles may look like Jews for their face or what they wear and they are as Gentiles as others. Looking Jewish, even if having in fact Jewish ancestors, means nothing. Except if your mother is Jewish.
And regarding converts, they don't have to LOOK Jewish, they must live as Jews (and only after having converted in front of a valid Beis Din).