In Harry Potter and the Prisoner of Azkaban, Harry is prevented from casting "Riddikulus" by Professor Lupin's interception, hence making the Boggart change its form.
If Lupin didn't intercept it, and Harry did cast the spell, what would the (humourous) end result have been?
My initial thoughts were that it would become a black blanket, or some black quill ink falling to the floor.
It depends on what the caster pictured when casting the spell. The form the boggart takes when the riddikulus charm is used isn't dependent on the form the boggart is in, it depends on what the caster has determined to change it into.
If you remember, both the book and the movie have Lupin instructing the class to imagine what they fear most and imagine a way to make it funny.
With Neville, he even asked what Neville feared most and told him what to imagine before casting the spell.
That said, we have no idea what Harry would have pictured for a dementor. Lupin interfered before we could find out. :-P
While David Stratton offers up a plausible (and perfectly in-cannon and correct) answer that makes a lot of sense, I'd like to offer another possible take on the matter.
In addition to the idea that what the boggart will appear as, is dependent on the individual casting the charm's thoughts, so there really is no way of knowing how it will appear for any particular individual, I would say that perhaps there are certain times when the Ridikulus charm doesn't work or isn't plausible.
Dementors represent fear itself. Lupin says so when discussing the matter with Harry. Lupin tells Harry he is impressed and surprised that Harry's worst fear is a dementor and this follows:
"He smiled slightly at the look of surprise on Harry's face. 'that suggests that what you fear most of all is - fear. Very wise, Harry.'"
Therefore, my thoughts were that there is no way to take the fear out of a dementor form and make them funny (there are a few things in life that cannot be made to be or look ridiculous after all). This would be one form a boggart could have the potential of taking that would cause the riddikulus charm not to work. After all, Mrs. Weasley is almost defeated by one when her boggart repeatedly appears as one of her loved ones dead causing a sense of grief to intermingle with her fear - something she is unable to make look ridiculous (and I dare-say, I'd have a tough one with that little challenge too).
It just shouldn't be as easy as making it look like a blanket (or smoke as wiki indicates in one location) or something - this is fear we are talking about.
Harry has more questions, but they are interrupted by Snape's entrance with "a potion he concocted" for Lupin and Harry's questions are left unanswered.
I'll grant that Lupin's given reason for interrupting Harry, is that he assumed Harry would see Voldemort and Lupin feared the reaction the rest of the class would have. However, I still like the idea that fear is one form of only a few that a boggart could take that would truly challenge even the bravest and/or smartest of wizards.
There is an instance in canon where Harry uses the Riddikulus charm on a Dementor Boggart with success.
During the Third task, namely the Maze, of the Triwizard tournament, Harry encounters a Dementor and casts a full corporeal Patronus. Overwhelmed, the "Dementor" trips over the hem of its robes, making Harry realise it is not one but only a Boggart. (Real Dementors float away at a Patronus, and their stumbling is just ridiculous.) He then casts the Riddikulus Charm to good effect:
"There was a loud crack, and the shape-shifter exploded in a wisp of smoke."
-Goblet of Fire, Chapter 31, The Third Task.
So this is what happens when the Riddikulus Charm is cast on a Dementor Boggart.
Note that this is the same as what happens finally in Lupin's class.
One may say that since a Dementor is fear "personified" according to Lupin, making it ridiculous is just having it disappear.
That said, one may also ask which is more ridiculous - having it explode in a wisp of smoke, or having it trip over the hem of its robes!
