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How can Light show dual Nature, It is just saying like, An animal is Dog as well as Cat

How can Light exist in dual Nature?,for instance,

when can The light show particle nature and when can it show Wave nature, in what circumstances It might show Wave nature but not particle one,and in what circumstances it might show particle nature but not wave. I am getting confused at That!Please help me understanding this I am not asking about reality of Dual nature of light,I know that light shows dual nature, but can't understand why is this so!!!

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Dheeraj, great volumes of stuff have been written about this, I recommend you do a search on wave-particle duality; in the meantime, here are the (simplified) basics.

The basic unit of light is the photon. Depending on its wavelength and what method you use to detect it, it can behave either as a wave or a particle. If you have a very very large number of photons (coming from a lit candle, for example) then those photons are most easily described in terms of waves with different wave lengths. If you have a very very small number of photons then they are most easily described as particles with different energies.

Photons can have wavelengths spanning the size range of bigger than kilometers to smaller than nanometers. When working with wavelengths between a kilometer and a centimeter and huge numbers of photons, the wave representation is almost exclusively used. By the time you get down to ~hundreds of nanometers for the wave lengths, wave and particle representations can be used almost interchangeably. Below a nanometer, the particle picture becomes more convenient.

The real picture is a lot more complicated than this and easily represents an entire semester or more of university-level physics. I invite the experts here to add to this answer if they have any other basic ways of explaining this.

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The basic experimental facts are usually discussed in the introductory chapters to quantum mechanics textbooks, since the discreteness of light (i.e., its particle-like properties) was one of the triggers for developing quantum theory. In particular, Planck assumed that light is quantized in order to regularize the divergences in the black-body radiation, whereas Einstein analyzed photoelectric effect. Compton effect is another case where light is best interpreted as particles with definite state and momentum.

To summarize:

  • Planck's law
  • Photoelectric effect
  • Compton scattering

The wave properties of light are beyond doubt, since it is described by Maxwell equations (and teh wave equations following from them).

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