What gives you the idea that I want them to do it? I just want to understand how "there is the" works.
You've already been given one main example - the idea of sudden realisation of where something is. However, native speakers wouldn't use "There is" in it; they'd use "There's".
I've been looking for my book for three hours when I suddenly spot it on a table. I exclaim "Ohhh!
There's the book!" The emphasis would be very strongly on "There's". You could add the location but there would be a pause in speech, and punctuation in writing. It would read "Ohhh!
There's the book
- on the table! I'm sure I looked there earlier."
The only other context I can think of is when giving a list of examples:
A: What big cats can you think of?
B: Well,
there's the lion, the tiger, the jaguar and the leopard. I can't think of any more.
A: What examples of printed material can you think of?
B: Hmm, let me think.
There's the book, the magazine, the newspaper, the journal, the pamphlet ... that's it. I don't know any others.
No matter how many times you ask, or come up with new examples, "There is the book on the table" will never be correct as a standalone sentence.