The function I use to translate a filename and given extension into it’s MIME type is available as a Provider in BmFB so that you can use my work for your app too.

    Uri theContentProvider = Uri.parse("content://com.blackmoonit.android.mimetypeprovider/getMIMEtype");
    Uri theContentTypeRequest = Uri.withAppendedPath(theContentProvider, aFile.getName());
    Cursor theTypeResult = managedQuery(theContentTypeRequest, null, null, null, null);
    theTypeResult.moveToFirst();
    if (!theTypeResult.isNull(0)) {
        String theMIMEType = theTypeResult.getString(0);
        ...
    }