# Destructive interference in Unpolarised light

• JohnHon
In summary: The output power is then distributed in a manner such that the total power is unchanged no matter where the antennas are pointed. So we have incoherent light.But what about Young's double slit experiment? That's where you have a beam of light that is split in two, with one half going to one side of the slit and the other half going to the other side. Assuming the electric field vectors are equal in magnitude at the two points, the beam of light should have zero intensity at the point where the two beams intersect. But obviously it doesn't. So how is it generating intensity?
JohnHon
Destructive interference is excellently demonstrated in Young's double slit experiment, where dark regions are formed due the waves being out of phase. However, what really confuses me is that unpolarised light has intensity.

Assuming we had perfectly unpolarised light, as in where the electric field vectors are equal in magnitude in every direction at a single point in space (basically different waves destructively interfering), how does that beam of light produce intensity? In fact for this perfectly unpolarised light beam, shouldn’t we detect nothing, as there is never a NET electric field and thus no intensity?

So can someone explain how somehow in the double slit experiment there is 0 intensity in destructive interference yet unpolarised light DOES have intensity?

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You're also assuming completely coherent light, so that each wave in each plane reaches the same intensity at the same instant. And you're assuming monochromatic light, so all the phase relationships are constant. Neither of those things is true with an ordinary light source. When waves add incoherently, their energies add.

JohnHon said:
Assuming we had perfectly unpolarised light, as in where the electric field vectors are equal in magnitude in every direction at a single point in space
Where did you find this definition of unpolarised light? It doesn't seem right to me. I'd agree that, over time, you will find the electric field vector at a given point does at some time point in every available direction, but the direction at a point at a single instant is well-defined. It just doesn't tell you anything about the direction at any other point, or at any other time.

Cryo
Unpolarized light simply means that polarization of light changes faster than the detection capability of your apparatus. It also means that polarization changes in a random fashion. But polarization at any instant is well-defined. When you start doing Young's interference you have (e.g.) two copies of electric field that you guided along different paths. Let's say that electric field on the screen is given by:

##\mathbf{E(t)}=\mathbf{E}_1 (t) + \mathbf{E}_2 (t)##

Where ##\mathbf{E}_{1,2}## are the electric fields guided along different paths. Let's simplify and say that the only difference between them is that ##\mathbf{E}_{1}=\mathbf{E}_0 (t-t_1)## and ##\mathbf{E}_{2}=\mathbf{E}_0 (t-t_2)##, where ##\mathbf{E}_0 ## is the original source. So we are saying the two interfering fields are simply routed through two delay lines.

If the source is random, there is usually some sort of coherence time ##\tau## within which the randomness of the source is negligible. So as long as ##t_2-t_1<\tau## you will see interference fringes. Note, than one often talks of coherence length ##L=c \tau##, where ##c## is the speed of light.

Interestingly, if we have a pure CW source we cannot obtain unpolarised radiation from it. A classical source of unpolarised light consists of two orthogonal antennas each driven by a noise generator.

## What is destructive interference in unpolarised light?

Destructive interference in unpolarised light occurs when two or more light waves of the same frequency and amplitude are out of phase with each other. This results in the cancellation of the waves, causing a decrease in the overall intensity of the light.

## How does destructive interference in unpolarised light differ from polarised light?

In polarised light, the light waves are all oriented in the same direction, while in unpolarised light, the waves are oriented in all possible directions. This means that in unpolarised light, the waves can interfere with each other in different ways, resulting in a more complex pattern of interference compared to polarised light.

## What causes destructive interference in unpolarised light?

Destructive interference in unpolarised light is caused by the superposition of two or more light waves. When the waves are out of phase, they cancel each other out, resulting in a decrease in the overall intensity of the light.

## How is destructive interference in unpolarised light used in everyday life?

Destructive interference in unpolarised light is used in a variety of everyday applications, such as in anti-glare coatings on glasses, LCD screens, and in noise-cancelling headphones. It is also used in spectroscopy to identify different substances based on the unique patterns of destructive interference they produce.

## Can destructive interference in unpolarised light be reversed?

Yes, destructive interference in unpolarised light can be reversed by changing the phase relationship between the interfering waves. This can be achieved by changing the path length of one of the waves or by using a polariser to change the orientation of the waves.

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