Get last delimiter with explode

You can use the pathinfo function with the PATHINFO_EXTENSION option to get exclusively this information.

$string = "adsfasdfasd.234.asdfa.3rfr.jpg";
echo pathinfo($string, PATHINFO_EXTENSION); // jpg

DEMO

Your code should look like this:

$diretório = getcwd(); // Diretório atual

if ($handle = opendir($diretório)) {
    while (false !== ($file = readdir($handle))) {
        if (is_file($file) && $file != "." && $file != "..") {
            $info = pathinfo($file);
            $arquivo = $info['filename']; // Nome do arquivo
            $ext = $info['extension'];    // Extensão
        }
    }
    closedir($handle); // Fecha o manipulador aberto por opendir()
}

Complementing what has been answered previously, there are some alternatives to pathinfo , just to show other ways of working with strings , given the high performance in case of simple operations of this type. / p>

Getting only the extension:

I did not use list combined with explode because it did not work correctly in case of several points in the middle of the name.

Using explode:

$ext = end( explode( '.', $file) );

Using string operations (preferred):

$ext = strrchr( $file, '.' ); // retorna do último ponto em diante .jpg

also:

$ext = substr( strrchr( $file, '.' ), 1); // retorna jpg (sem o ponto)

or even:

$pos = strrpos( $file, '.' );
$ext = ( $pos === false ) ? '' : substr( $file, $pos + 1 );

Getting extension and filename:

$pos = strrpos( $file, '.' );
$ext = ( $pos === false ) ? '' : substr( $file, $pos + 1 );
$arq = ( $pos === false ) ? $file : substr( $file, 0, $pos );

See working at IDEONE .