Maybe you could use String#split
To answer your comment:
I'm not sure if there can be more than one . in a filename, but whatever, even if there are more dots you can use the split. Consider e.g. that:
String input = "boo.and.foo";
String[] result = input.split(".");
This will return an array containing:
{ "boo", "and", "foo" }
So you will know that the last index in the array is the extension and all others are the base.