Amplitude of light waves

We know from intuition that a wave has a property called Amplitude. I am also convinced that the Amplitude of a water wave decreases slowly when it is far from its source/ I.e.when the wave is spread.

But what I find confusing is when light spreads far from its source, is the Amplitude of the light wave decreased?

Yes, in water waves, some disturbance in it's STILL state caused the introduction of the wave, and as I've been taught and yes has accepted that it's because of property of friction the Amplitude decreases and the wave finally vanishes.

So, my question, seeking a satiable answer is as follows, I hope you will help me.

1. Why in case of light, the Amplitude doesn't seem to decrease when it travels in vacuum(even though electric and magnetic fields from nearby sources exists)?

2. It is said that from Maxwell's wave equation, light is a transversal wave. So, when we draw a light wave, the changing electric field is drawn mutually perpendit to the changing magnetic field. The Amplitude is the highest value of the function, but physically, the value keeps on increasing and after reaching a certain point(the Amplitude) decreases again upto it's negative value, where does the light gets its energy to again oscillate from its negative Amplitude to the positive Amplitude.

I'm not sure where do light gets its energy for oscillation.

• I can’t answer 1., because the amplitude of electromagnetic waves indeed decreases when they they spread away form the source. Otherwise, far away light sources would be as bright as nearby sources! I don’t get why, for you “he Amplitude doesn't seem to decrease when it travels in vacuum” – Frédéric Grosshans Oct 19 '16 at 9:39
• ad 1: The amplitude of light which you are talking about is the Intensity, which does decrease with increasing distance ad 2: The electromagnetic wave in simple words is a periodic conversion from electric to magnetic energy and vice versa – counter Oct 19 '16 at 9:55
• I was wondering if they decrease their Amplitude with distance, then when we look up at the sky and see a star we say that we are seeing light from the past because it has reached here after a long time. So, for that particular wave it has not been completely vanished because we are able to see. So, I was wondering if the Amplitude had not decreased with distance – Jyotishraj Thoudam Oct 19 '16 at 9:58
• Now the stars you are seeing in the sky are like the sun but mostly bigger. Have you ever tried looking directly at the sun? (Don't do it!) The sun is extremely bright - so are these stars, but due to the distance you can look at them without going blind. – counter Oct 19 '16 at 9:59
• So, how far we have to be so that the Amplitude vanishes completely and we are not able to see the wave? – Jyotishraj Thoudam Oct 19 '16 at 10:09

"Why in case of light, the Amplitude doesn't seem to decrease when it travels in vacuum(even though electric and magnetic fields from nearby sources exists)?"

Perhaps the confusion is caused by the concept of a plane wave. Yes, indeed, a plane wave has an amplitude that remains constant throughout space. However, one never finds an exact plane wave in practical situations. Practical optical beams always have a finite transverse scale. You can think of the optical beam produced by a laser point. The spot of light that it produces has a finite size. As a result this beam will gradually expand as in propagates further and further.

In general on can have cylindrical waves or spherical waves, in addition to plane waves. The conservation of energy dictates that total power on a closed surface perpendicular to the direction of propagation must be constant regardless of far away that surface is (assuming of course there is no absorption of the optical power along the way). Power is the integral over the intensity over an area and intensity is proportional to the square of the amplitude. To satisfy this requirement the amplitude of a cylindrical wave must decrease as one over the square root of the radius of the cylindrical surface. On the other hand, for the spherical wave the amplitude decreases as one over the radius spherical surface.

Next question:

"It is said that from Maxwell's wave equation, light is a transverse wave. So, when we draw a light wave, the changing electric field is drawn mutually perpendicular to the changing magnetic field. The Amplitude is the highest value of the function, but physically, the value keeps on increasing and after reaching a certain point(the Amplitude) decreases again up to it's negative value, where does the light gets its energy to again oscillate from its negative Amplitude to the positive Amplitude."

Some times the diagram could perhaps be misleading. The typical diagram showing the electric and magnetic fields represents the spatial shape of the fields as they are frozen in time. However, if one were to turn on the evolution of this field in time, how would the diagram change? It would shift in the direction of propagation. This is the basic property of a wave. If the frozen diagram for the electric field for instance is represented by a function $\mathbf{E}(z)$, then the corresponding expression for the electric field as it evolves in time is represented by $\mathbf{E}(z-ct)$. So we see that the function shift toward the direction of propagation (positive $z$-direction in this case) at the speed of light.

One can now use this evolution to see what would happen if we look at just one point in space and see what the electric field does as a function of time. So let's set $z=0$, then we get $\mathbf{E}(-ct)$. So we see that we get the same function but as a function of time and now it is inverted. The the electric field oscillates at any particular point in space.

The energy in the field is carried along with it. One can calculate the energy by integrating the power over time.

Hope all the issues have been addressed. Let me know if anything is still unclear.

A wave is something which can transfer energy and momentum without bodily moving the medium through which it is travelling.
The oscillation of the electric and magnetic fields moving along is an electromagnetic wave.

For a point source, with no absorption by the medium through which the wave is travelling, the amplitude of the wave is proportional to the reciprocal of distance of the wave from the point source and the intensity (power per unit area) follows an inverse square law.
That being the case as the distance gets very large the amplitude will get very small.

In theory and assuming that light travels in straight lines, if you have a parallel beam of light the light amplitude/intensity will not drop but you cannot have such a beam in practice and the light intensity will drop with distance.

If you have a laser pointer you will observe that the spot of light produced by the laser gets bigger and less bright when you shine it on objects which are further away.

This is the classical picture and what happens at very large distance might be clearer using the quantum mechanical picture with light being considered as a beam of photons.

From a point source photons are emitted in all direction and the intensity of the light is related to the number of photons which go through unit area per second.
Normally there are so many photons arriving per second that you do not detect individual photons but rather the average effect of lots of them arriving per second.

Going further and further from a point source the number of photons which arrive per second decreases to such an extent that for very distant light sources (galaxies) the photomultiplier tubes detecting the photons can register individual photons arriving.
So "finally vanishing" means that the photomultiplier tube has not detected any photons over a period of time.
If you waited longer a photon might be detected or it might be that at that distance all the emitted photons have interacted with matter.

Light is emitted in packages

From any source, be this a star or a bulb or a laser or something else, light is emitted as quanta, later called photons. This has to do with the excitation of subatomic particles, mostly electrons. They absorb and re-emit photons.

Photons are indivisible units and as you stated well they have an oscillating electric field component and an oscillating magnetic field component. Because of the existance of this field components photon radiation is called also electroagnetic radiation (EM radiaten).

For electromagnetic radiation from thermal sources it isn't possible to measure a common for all the included photons oscillation. Their time of emission is randomly distributed and their electric and magnetic field components are pointing by 90° to each other but they are equally distributed all over 360°. That is why stars emit EM radiation.

An EM wave you get from an antenna where the photons get emitted nearly at the same time, all are polarized and the emission itself is with an oscillating intensity.

Energy content of photons

Photons are indivisible, always have the two field components and all are moving with the speed of light. But the are distinguishable by their energy content. The greater the energy content the more energy will be realized than the photon gets absorbed. The same amount of infrared photons will heat a black body less than ultraviolett photons. In this sence one can talk about the photons intensity. Intensity is not a dimensional property, it is a quantitative property.

Intensity and amplitude

The theory stated that electric and magnetic fields are extended to infinity. To talk then about an amplitude like for water waves makes no sense.
A photons can go through a wide enough slit undisturbed. The smallest slit for which this is possible is somehow associated with a cross section of a photon and not with an amplitude.

But there is the famous double slit experiment there the intensity of an incomming EM radiation gets converted into an intenisty distribution behind the slits. The intensity of each fringe is measurable and if one draw a graph this graph will looks like a wave. It is stated that the amplitude of this graph and the intensity of the light are related.

Intensity of EM radiation and of photons over distances

A far away star emits photons in all directions. Over distances this EM radiation gets weaker and weaker. To collect the light from stars billion light years far away from us one exposure the measurement instrument by hours to collect enought photons. So the intensity of EM radiation decreases other distances.

Photons are indivisible units and the travel through space invisible (without interaction) as long as they not hit matter, for example the measurement instrument. Since the photon does not lose energy during his travel, the intensity of the photon stays the same.