As Newton's law gives rise to the way we analyse linear motion , circular motion and simple harmonic motion. Principle of superposition enable us to explain stationary wave fromation, young double slit expt(2slit) and diffraction grating expt.(multiple slit) and diffraction(1 slit) .
In stationary wave the two waves that interfere and then superpose is rather complicated and changes with time (worse still , their veolcity is opposite in direction) and therefore you only need to know the final result . Like using a calculator to do addition is so easy. So having learnt adding simple waves like A+A = 2A and then A-A = 0 , we just use calculator and voila you get stationary wave effect that changes with time. Just know the final effect .
In Young double slit , putting the screen very far , you get bright and dark fringes because the slits are straight . Imagine if they are two holes what would you see? Imagine they are two speakers instead of two slits what would you see ??or hear? Coherence is simple if you know that two speakers playing independently would not produce anything permanent for you to detect. The two speakers got to play a tune which is of the same frequency and constant phase difference(normally mean in phase seldom out of phase ) if the output from your sound machine is split to two speakers. In light source it sounds more abstract , you need to split one light source into two Therefore you use single slit first and then double slit to produce two coherent source.
To explain why certain spots are bright and dark , you would have to employ your principle of superpostion .
Bright : Two waves interfere constructively (A+A=2A) as both the waves arriving there are in phase , the intensity of each source is I and at the location where it is bright the intensity is 4I. which is 4times.
Dark: Two waves interfere destructively (A-A-0) as both waves arriving there are out of phase, the intensity at the location is 0 , meaning no intensity.
When mulitple slits called diffraction grating is used, the explanation for bright fringes formed are the same but we normally do not mention about the dark fringes. No screen is used so the fringes at measured at angles from the central bright fringe (n=0) . Using the formula dsin 8=n /\ as a calculator, you can locate the bright fringes are formed. Each colour having its own unique angle from the central bright fringe. If two colour having the same angle , an overlap is said to have occured. Overlap is not possible in the first order colour fringes. If a single colour light is used overlap is also not possible. The max order possible is one with an angle below 90 degrees.
