$(a)$ 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. Explain why?
$(b)$ When light travels from a rarer to a denser medium,the speed decreases. Does the reduction in speed imply a reduction in the energy carried by the light wave?
$(c)$ In the wave picture of light,intensity of light is determined by the square of the amplitude of the wave. What determines the intensity of light in the photon picture of light?

(N/A) Reflection and refraction arise through the interaction of incident light with the atomic constituents of matter. Atoms act as oscillators that take up the frequency of the external agency (incident light),resulting in forced oscillations. Since the frequency of light emitted by a charged oscillator equals its frequency of oscillation,the frequency of reflected and refracted light remains equal to the incident frequency.
$(b)$ No. The energy carried by a wave depends on the amplitude of the wave,not on the speed of wave propagation. Therefore,a reduction in speed does not imply a reduction in energy.
$(c)$ In the photon picture of light,the intensity is determined by the number of photons crossing a unit area per unit time for a given frequency.