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.
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)?
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.
Please help me clarify this.
Answer
Let's look at your question
"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.
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