(function() {

    var extToMimes = {
       'img': 'image/jpeg',
       'png': 'image/png',
       ...
    }

    window.getMimeByExt = function(ext) {
        if (extToMimes.hasOwnProperty(ext)) {
           return extToMimes[ext];
        }
        return false;
    }

})();

var mime = $('input[type="file"]').prop('files')[0].file;

<script src="https://wzrd.in/standalone/mime@latest"></script>
<script>
    mime.getType("something.pdf"); // etc.
<script>