Huygen’s Principle & its Applications

Presented By:- VivekKumar :- Bs-Ms (1st Year)

ContentsIntroduction Huygen’s Principle Applications of Huygen’s Principle to the study

Refraction And ReflectionTotal Internal Reflection Diffuse Reflection Summary

IntroductionThe wave theory of light was 1st forward by

Christiaan Huygens in 1678.During that period , everyone believed in

Newton’s Corpuscular theory, which had satisfactorily explain the phenomena of reflection, refraction, the rectilinear propagation of light and the fact that light light could propagate through vacuum.

The Corpuscular model predicted that if the ray of light (on refraction) bends towards the normal then the speed of light would be greater in the second medium.

In 1678, the Dutch Physicist Christiaan Huygens put forward the wave theory of light-it is wave model of light.

The wave model could satisfactorily explain the

Phenomena of reflection and refraction;However, it predicted that on refraction if the wave Bends towards the normal then the speed of light

would be less in second medium.According to Maxwell, light waves are associated

with changing electric & magnetic field; changing electric field produces a time and space varying magnetic field & a changing magnetic field produces a time and space varying electric field.

The changing electric & magnetic field result in the propagation of electromagnetic waves (or light waves) even in vaccum.

Huygen’s Theory Wavefront

It is the locus of points on a wave having sane phase .Direction of waves is always perpendicular to the

wavefront. o For a point source wave front is spherical, o For a line source wave front is always cylinderical o In case of plane soutce wave front is always palne.If point source & line source placed at ∞ then

wave front always appears to be plane. For Example

If we drop a small stone in a calm pool of water, circular ripples spread out from the point of impact, each point on the circumference of the circle (whose centre as at the point of impact) oscillates with the same amplitudes & same phase

and same phase and thus we a circular wave front.At large distance from the source, a small portion of the sphere can be considered as a plane and we have what is known as a plane wave .

Spherical wavefront Cylindrical wavefront Plane wave front

Spherical wave front Cylindrecial wave front

Huygen’s Principle It is a Geometric Constructions used to find

the shape and position of new wave fronts at a given instant of time . It is base on the following assumption:-All points are primary wave front act as a source for the formation of secondary wave front.Velocity of wave from primary to secondary wave front is same as that from the source of the primary wave front.

We always taking to consideration the forward wave front and ignore the backward wave front because energy always propagate in forward direction.

Reasons :-

In Huygen’s theory , the presence of the backward Is avoided by assuming that the amplitude of the

secondary wavelets is not uniform an all directions ; it is maximum in the forward direction & zero in the backward direction.

Reflection of a plane wave by a plane surface Consider a beam of light incident on a

plane surface at points P,Q,R and getting reflected

As shown in fig.Primary & Secondary wave front are

drawn along perpendicular to the incident and reflected rays.

Time = Distance/SpeedT= MQ+QS/CT= PQ sini + QR sinr/CT= PQ sini + (PR-PQ)sinr/C

T= PQ(sini + sinr) + PR sinr/CPosition of Q is not fixed , time taken will not

depend upon term PQ.PQ(sini + sinr) = 0But PQ is not equal to zeroSini – sinr = 0Sini = sinr Hence , angle of incidence is equal to the angle of

reflection.( Henced Proved)

Refraction of a Plane Wave

Time= Distance/SpeedT= MQ/C + QS/VT= PQ sini/C + QR sinr/VT= PQ sini/C + (PR-PQ)sinr/V

T= PQ(sini/C + sinr/V) + PR sinr/VPosition of Q is not fixed , time taken will not

depend upon term PQPQ(sini/C + sinr/V) = 0But PQ is nor equal to zeroSini/C + sinr/VSini/C = sinr/VSini/sinr = C/V=µHence, snell’s law is proved(Henced Proved)

Total Internal Reflection (TIR)In above fig. the angle of incidence has been

shown to be greater than the angle of incidence. This corresponds to the case when V2<V1, i.e, the light wave is incident on denser medium.

If the second medium is a rare medium (i.e, V1<V2) then the angle of refraction will be greater than the angle of incidence. Where B1B2= V1t and A1A2= V2t.

Clearly , if the angle of incidence id such that V2t is > than A1B2 , then the refracted wave front will be absent and we will have, what is known as , TIR.

THE CRITICAL ANGLE WILL CORRESPONDS TO A1B2 = V2t

Thus sinic = B1B2/A1B2 = V1/V2 = n12Where, ic denotes the critical angle and n12

represents the refractive index of the second medium w.r.t the 1st.

For all angles of incidence greater than ic , we will have total internal reflection. Diffuse Reflection

In the above we considered the reflection of light from a smooth surface. This is known as specular reflection.

If the surface is irregular we have , what is known as diffuse reflection.

The secondary wavelets emanating from the irregular surface travel in many directions and we do not have a well defined reflected wave.

If the irregularity in the surface is considerably greater than the wavelength, wee will have diffuse reflection.

SummaryAccording to Hugyen’s Principle, each point of a wave front is a source of secondary disturbance and the wavelets emanating from these points s[read out in all directions with the speed of the wave. The envelope of these wavelets gives the shape of the new wave front. Huygen’s Principle along with the fact that the secondary wavelets mutually interfere , is known as the Huygen’s – Fresenel Principle. Law’s of reflection and Snell’s law of refraction can be derived using Huygen’s Principle. Using Huygen’s Principle one can derived the lens fomula

1/v – 1/u = 1/f.

Thank-you