Current file line number with $. variable

Question

I understand that I can get the current line number of a file I am looping through with the builtin variable $.. As an experiment, I used that to prefix each line in a file with the value of $. (the current line number). However, this did not work as expected. I.e., given the following file contents

line one
line two
line three

then I would expect the following code to prefix each line with its line number

for my $line (<FILE>) {
    print "$. : $line";
}

but, instead, it gives the following output

3 line one
3 line two
3 line three

prefixing each line with the number of lines in the file. Instead of the current line.