Mirth is amusement which you express by laughing. That caused considerable mirth amongst pupils and sports masters alike = hilarity. Gladness and gaiety, especially when expressed by laughter. happiness and laughter
full of or showing high-spirited merriment; "when hearts were young and gay"; "a poet could not but be gay, in such a jocund company"- Wordsworth; "the jolly crowd at the reunion"; "jolly old Saint Nick"; "a jovial old gentleman"; "have a merry Christmas"; "peals of merry laughter"; "a mirthful laugh"
arousing or provoking laughter; "an amusing film with a steady stream of pranks and pratfalls"; "an amusing fellow"; "a comic hat"; "a comical look of surprise"; "funny stories that made everybody laugh"; "a very funny writer"; "it would have been laughable if it hadn't hurt so much"; "a mirthful experience"; "risible courtroom antics"
If someone gives a mirthless laugh or smile, it is obvious that they are not really amused. mirthless laughter or a mirthless smile does not seem to be caused by real amusement or happiness