When monochromatic light is incident on a surface separating two media the reflected and refracted light both have same frequency as the incident frequency give reason?

It's actually important to recall that this is true only by definition, because it's part and parcel of what refraction means. But refraction is not the only thing that can happen when light passes between two mediums, even though it is probably by far the most common thing that happens in this situation.

There are solutions of Maxwell's equations where light passes between two mediums and the interaction of electromagnetic field and medium is linear, and, experimentally, we observe these interactions often and in keeping with Maxwellian theory. In such a case, the physics is as described by John Rennie's Answer.

But intense beams incident on a frequency doubling or other nonlinear material, where the physics is no longer linear, do not conserve the frequency. Hence my somewhat pedantic point about being true by definition. One can't prove that frequency is conserved in general, as shown by the nonlinear counterexamples.

Explain the following, giving reasons :i When monochromatic light is incident on a surface separating two media, the reflected and refracted light both have the same frequency as the incident frequency.ii When light travels from a rarer to a denser medium, the speed decreases. Does this decrease in speed imply a reduction in the energy carried by the wave?iii In the wave picture of light, intensity of light is determined by the square of the amplitude of the wave. What determines the intensity in the photon picture of light?

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