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In many books it is written that light is an electromagnetic wave, as we know there does not exist any oscillator that can oscillate an electron with a frequency of light.

My question is, how can we prove that light is electromagnetic in nature ? what is light ? is there any physical meaning.

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This question comes from a false premise.

To say "you can't oscillate an electron at the speed of light" is like saying you can't drive a car at the temperature of boiling water. They're not measuring the same thing. Oscillation is a measure of cycles-per-unit-time. Speed is a measure of distance-per-unit-time. They're different things with different units.

We can absolutely oscillate electrons at the frequency of light. That's how radios work. A properly functional radio is proof that light is electromagnetic in nature. If light wasn't electromagnetic then it wouldn't induce a current in a radio antenna.

"What is light?" is a philosophical question with many different answers depending on the context. That's because a single "thing" can have multiple definitions. You could say the USA is "the country founded by George Washington" or "the nation-state immediately south of Canada" or "the federal republic formed in 1789". All three definitions refer to the same United States of America.

In physics, the word "light" has a well-defined physical meaning. But there's multiple ways of defining that one thing. You can define light as "electromagnetic wave", "photons" or "that stuff a lamp shoots at you". Which definition you use depends on who you're talking to and what you're talking about.

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    $\begingroup$ The frequency of radio waves is a lot lower than that of visible light. $\endgroup$ – PM 2Ring Jun 9 '19 at 10:33
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how can we prove that light is electromagnetic in nature ?

The easiest way is to observe that it interacts with charged particles. The electromagnetic force is by definition the force that acts on charged particles. Furthermore, it is a long range force, unlike the strong and weak forces which act only over nuclear distances. So light acts at long distances and interacts with charged particles, therefore it is an electromagnetic force.

Besides this, it behaves as expected regarding electromagnetic interactions with materials. It is reflected by smooth conductors and dielectrics, and when it is reflected from dielectrics it becomes polarized.

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The first indication was that the speed of light matches that predicted by Maxwell's electromagnetic equations.

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as we know there does not exist any oscillator that can oscillate an electron with a frequency of light

Wrong. There does exist such an oscillator, it's called wiggler, and is used in the free electron laser. Depending on magnetic field, velocity of the electron beam and period the magnet arrangement, it can generate a wide range of EM frequencies.

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If two electrons in serial move in a resistance because of a voltage, then voltage makes them to move very close, whereas the electric fields of the electrons repel. So, there is a strain in electric field and light energy is released. Electric field between these two electrons in serial satisfies Maxwell equations. So, light waves may be considered as electromagnetic waves.

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