(a) State Huygen's principle . Using this principle draw a diagram to show how a plane wave front incident at the interface of the media gets refracted when it propagates from a rarer to a denser medium. Hence verify Snell's law of refraction.
(b) When monochromatic light travels from a rarer to a denser medium, explain the following, giving reasons-
(i) Is the frequency of reflected and refracted light same as the frequency of incident light?
(ii) Does the decrease in speed imply a reduction in the energy carried by light wave?

Explanation

(a) Huygen's Principle : It is based on the two assumptions:
(i) Each point on the primary wave front acts as a source of secondary wavelets, sending out disturbance in all directions in a similar manner as the original source of light does.
(ii) The new position of the wave front at any instant is the envelope of the secondary wavelets at that instant.
Refraction On the Basis of Wave Theory
(i) Consider any point Q on the incident wave front.
(ii) Suppose when disturbance from point P on incident wave front reaches point P' on the refracting surface XY.
(iii) Since, P'A' represents the refracted wave front, the time taken by light to travel from a point on incident wave front to the corresponding point on refracted wave front should always be the same. Now, time taken by light to go from Q to Q' will be
`t=(QK)/(c)+(KQ')/(v) " " `...(i)
In right angled `Delta AQK, lt QAK =i`
`therefore QK=AK sin i " " `...(ii)
In right - angled `Delta P'Q'K, lt Q'P'K= r and KQ' =KP' sin r." " ` ...(iii)
Substituting (ii) and (iii) in equation (i),
we get
`t=(AK sin i)/(c) +(KP'sin r)/(v)`
`" Or " t=(AKsin i)/(c) =((AP'-AK)sinr)/(v) " " (therefore KP'=AP'-AK)`
` "Or " t = (AP')/(c) sin r+AK((sinr)/(c)-(sinr)/(v)) " " ` ...(iv)
The rays from different point on the incident wave front will take the same time to reach the corresponding points on the refracted wave from i.e., t given by equation (iv) is independent of AK. It will happen so,
If `(sin i)/(c) - (sin r)/(v)=0 rArr (sin i)/(sin r) =(c)/(v)=mu =(sin i)/(sin r)`
This is the Snell's Law for refraction of light.
(b) (i) The frequency of reflected light remains same as the frequency of incident light. Frequency only depends on the source of light.
(ii) Since, the frequency remains same, hence there is no reduction in energy.