I would like to know if it is necessary for me to specify it like this:
All of the major five browsers look in the site's root for a file named exactly favicon.ico, regardless of type, automatically.
You can override this with a link element with rel="icon", or rel="shortcut icon". The latter is supported by every browser, while the former is more correct, but not recognised by Internet Explorer.
Most browsers these days will look for a favicon.ico file on the root of the site.