Question

Why Interfarance ocurs in wave or light?

Answer 1

Hopefully you have taken trigonometry because that is the easiest way to define it.
If you want to write the equation for a wave the shape is best approximated through trigonometric functions like sine or cosine. The reason for this is visually pretty obvious. Look at the plot for a wave modeled by cos(x).
http://www.wolframalpha.com/input/?i=plot+cos%28x%29
now imagine another wave comes in with a different phase and/or frequency like cos(x+2)
http://www.wolframalpha.com/input/?i=plot+cos%28x%2B3%29
if we have the two run into each other we can basically simply add the two equations: cos(x)+cos(x+2)
http://www.wolframalpha.com/input/?i=plot+cos%28x%29%2Bcos%28x%2B2%29
Which you can see in the link is a different wave from either one. That is the most basic idea of interference.

Answer 2

constructive interference can be considered as one wave helping the other to have a higher amplitude (height of the wave). The two amplitudes simply add together. When a crest hits a crest, they add and when a crest hits a trough, they cancel each other out.

Run some water in the bath tube and sit in it. Move your legs back and forth with the waves and you will see that the waves generated get bigger and bigger. If you all of a sudden move your legs against the motion of the wave, you will see that the wave dies out pretty fast and you begin to make a new set of waves based on you new harmonic motion.

Answer 3

The really important underlying idea is the Superposition Principle: the idea that waves "add up".

Put roughly, if W1(x) and W2(x) are waves in a 1-D space for instance, then the two interfere with each other by the resulting wave is (W1 + W2)(x) = W1(x) + W2(x)

So one wave can add up on another and amply it; and a wave can add up negatively with another wave and partially or completely cancel it out.