There are many different kinds of invisible inks out there, a general answer may not include the specific one you have in mind, but I'll give you a quick overview concerning invisible inks.
Sometimes making an invisible ink visible doesn't involve a chemical reaction. For example if you use soap or a laundry detergent as invisible ink, you need ultraviolet (UV) light to make the writing visible. UV light is not visible, it has a shorter wavelength than humans can see. In this case the invisible ink 'glows' when you look at it with the right light source. This could be considered an invisible ink that relies on physics rather than chemistry.
Other invisible inks can be made visible by heating or spraying something on the piece of paper in question. These inks are most commonly used in mystery novels. They involve chemical reactions. For example phenolphthalein is a colorless liquid if you have a water-based solution. If you write something and then expose the paper to e.g. ammonia, the writing becomes visible (pink). This is an example in which the neutral molecule and it's anionic form have different colors. Exposing the paper to ammonia, deprotonates the phenolphthalein in the invisible ink, the hydrogens are removed from the hydroxyl groups and a ring opening reaction takes place, this changes which part of the visible light is absorbed by the molecule and it looks pink. An example of an invisible ink that can be made visible by heating is lemon juice. Lemon juice contains an organic acid and if you heat the writing the acid decomposes and you are left with carbon on the paper, this is what you see. You basically destroy the acid by burning it. This is of course an irreversible process. Once the message is visible it stays visible.
I hope this gives you a little bit of an idea about the variety of invisible inks available. Whole books have been written about this topic. If you are interested to know more, you should check your local library.Thank you for asking such an interesting question,
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