Hi Dinghui, the word 'right' in 'right now' and 'rightly so' serves different functions. When we say 'rightly so,' we mean something is correct or somebody did something correct. So in this context, Newton was correct in theorising that different colours are essentially different wavelengths of light. Another example could be: A: did you hear she has quit her job? B: yes, and rightly so- she was always under appreciated by her boss. (She did the right thing quitting her hob because her boss never appreciated her.)

In “rightly so”, “rightly” is an adverb meaning “in a right manner”, “correctly”. That is a normal usage of an adverb of manner formed by adding -ly to an adjective. “Right now” (right then, right on, etc.), on the other hand, is an idiomatic expression. Here, “right” is an adverb meaning “exactly”. In some cases, it’s the same either way, for example: “You guessed rightly / right”. In spoken English, we usually use “you guessed right”. Such “flat adverbs” were the norm in English until just a couple of hundred years ago (the blink of an eye in linguistic terms). Check out the Wikipedia article, if you’d like: https://en.wikipedia.org/wiki/Flat_adverb