(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

Explanation

When a monochromatic light (i.e. a light with single wavelength and hence single frequency) is made incident on a surface, separating two media, it interacts with atoms of medium. Here electrons in these atoms start oscillating under the influence of electric field in the incident light. We know that oscillatory motion is always an accelerated motion and any charged particle performing an accelerated motion, becomes the source of electromagnetic radiation. Light ray emitted this way, when propagates in the first medium in which incident light ray propagates), becomes reflected ray and when it propagates in the second medium, becomes refracted ray.
Here, frequency of reflected and refracted light ray are equal to frequency of oscillation of electron which is equal to frequency of oscillations of electric field which is equal to frequency of incident light. Thus, if fi fpf, represent frequencies of incident, reflectected and refracted light ray then, `f_(i)=f_(l)=f_(r)`
Energy carried by any wave depends on frequency of oscillation and amplitude of oscillation, but it does not depend on the speed of propagation in a given medium. Hence, when light ray enters from rarer to denser medium, reduction in its speed does not imply reduction in energy.
(c) According to definition of intensity of light, `I=(E)/(At)=` Amount of radiant energy incident perpendicularly on unit area per unit time.
Now, in photon picture of light, radiant energy is in the form of stream of different no. of photons of radiations of different frequencies.
For a given frequency f, radiant energy can be taken equal to n no. of photons. Hence E=nhf and so:
`I=(nhf)/(At)=n.hf`
Where `n.=(n)/(At)=` no. of photons made incident on unit area per unit time.
hus, in the photon picture of light, intensity of light depends on no. of photons made incident on unit area per unit time.