As mentioned you can use either index or a regex. If you are specifically looking to check a file extension, you'll want to ensure that the extension is at the end of the string. (That is, you don't want "file.htm.txt" to show up as a .htm file.)
The Regex way: Corrected, as I too fell for the .

$ext="\.htm";
if($file=~ /$ext$/){
     #Extension is at end of file
     # The final $ matches the end of the string.
}
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The edit way:

if((index ($filename, $ext) + 1 + length($ext))==length($filename)){
      #Extension was at end of $filename
      #Untested, I might be off by one
}
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