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I want to understand what is the physical significance of negative amplitude of a light wave?

In an ac electrical circuit, I understand that negative amplitude signifies the amplitude measured when the electron flow direction is reversed. Now it is easy to visualize and interpret.

Now in a light wave, what does it even mean by negative amplitude? Again, same question with respect to electro magnetic waves?

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    $\begingroup$ Other than "The electric force on a positively charged particle is in the negative x direction"? $\endgroup$ – Jerry Schirmer Jan 23 '15 at 22:39
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Exactly what means when you throw a pebble in the water of a lake. A wave appears, and you see that there are "valleys" and higher parts, that spread in circles. There where are valleys the level of the water is negative with respect to the original surface of the lake, and where there are higher parts the level is bigger (positive) than the original surface.

The only difference between the water waves and the light waves, is that in the light, what oscillate are the electric and magnetic field, see picture (electric field - blue, magnetic - pink). To see how these fields evolve in time see e.m. waves .

e.m. waves

In the water, if you look at a fix point you see the water going up, reaching a maximal height, then going down, reaching the minimum (most negative level) and so on. With the electric (and magnetic) field in the light it goes the same - look at the figure in the e.m. waves . At a given point in space the electric and the magnetic field increases getting maximally positive, then decreases up to maximally negative, and so on. Just pay attention - the pictures for the e.m. field correspond to linear polarization. Sometime you will learn about circular and elliptic polarization.

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Negative and positive are the same thing. When dealing with how the intensity of light (how brightly/darkly) plays out, you get the intensity of the electromagnetic wave. This is proportional to the square of the electric field, so it is always greater than $0$ (never 'negative').

If the electric field 'wave' has a 'negative' amplitude, it just signifies that the electric field vector at that particular point is in the opposite direction of positive.

Is this what you were looking for?

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"Positive" and "negative" are conventions - if we decide "this way" is positive, then "the other way" is negative. For any kind of simple harmonic oscillatory motion, deflections will spend equal amounts of time pointing in positive and negative direction. In the case of simple harmonic motion, we can say that the amplitude $A$ at time $t$ is given by

$$A(t) = A(0) e^{-i\omega t}$$

Where $\omega$ is the angular frequency. From this it follows that when $A(t)=-A(0)$, then $e^{-i\omega t}=-1$ so $\omega = \pi \mathrm{(modulo\ 2\pi)}$. In other words, it means there is a 180 degree phase shift compared to the "normal" positive amplitude. For a traveling wave, you can always find a point in time or space that's 180 degrees out of phase with another point - and if we say one of these points has positive amplitude, then the other has negative amplitude.

It is no different for an electromagnetic wave like light than it is for a pendulum.

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