Does Unpolarized Light Cancel Out Due to Mixed Angles?

[Kidphysics]

Homework Statement

Hello, I am reading an intro book on optics and it is discussing the polarization of light and unpolarized light. My question is with unpolarized light I quote:

"This sinusoidally varying electric field can be thought of as a length of rope held by two children at opposite ends. The children begin to displace the ends in such a way that the rope moves in a plane, either up and down, left and right, or at any angle in between."

So with this in mind I think well if most light is naturally unpolarized then wouldn't a mix of all of the different angles eventually end up cancelling each other out? I'd like to think of polarized light as coming in two orthogonal basis and then all others combinations of the two, are all polarized light vectors the sum of basis components like force vectors? I'm still beginning so I appreciate the input.

Homework Equations

not sure

The Attempt at a Solution

looked at the wikipedia article and another website which is how I obtained the quote

 

[rude man]

It's a good question, and the reason the fields don't cancel each other is that light intensity goes as the square of the electric field vector.

And so a randomly varying field vector will produce intensities proportional to the square of the magnitude of the field, irrespective of orientation. And since the direction is random you can't find a second field vector of equal but opposite magnitude source to cancel the first, because on average their total field would increase by sqrt(2) and their intensity double.

If daylight or lamp light were polarized we'd be in big trouble though, since then two oppositely directed field vectors would cancel and give zero light. That's why interference works, and needs polarized light to happen.