1. Huygen’s Principle & itsApplications
PresentedBy:- VivekKumar
:- Bs-Ms (1st Year)

2. Contents
Introduction
Huygen’s Principle
Applications of Huygen’s Principle to the study
Refraction And Reflection
Total Internal Reflection
Diffuse Reflection
Summary

3. Introduction
The 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

4. 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.

5. Huygen’s Theory
Wavefront
Itisthelocusofpointsonawavehavingsanephase.
Directionofwavesisalwaysperpendiculartothewavefront.
o Forapointsourcewavefrontisspherical,
o Foralinesourcewavefrontisalwayscylinderical
o Incaseofplanesoutcewavefrontisalwayspalne.
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

6. 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 .
Sphericalwavefront Cylindricalwavefront Planewavefront
Sphericalwavefront Cylindrecialwavefront

7. 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.
 Wealways taking to consideration the forward wave front and ignore
thebackward wave front because energy always propagate in forward
direction.
 Reasons :-

8. 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.

9. Time = Distance/Speed
T= MQ+QS/C
T= PQ sini + QR sinr/C
T= PQ sini + (PR-PQ)sinr/C

10. T= PQ(sini + sinr) + PR sinr/C
Position of Q is not fixed , time taken will not depend upon
term PQ.
PQ(sini + sinr) = 0
But PQ is not equal to zero
Sini – sinr = 0
Sini = sinr
Hence , angle of incidence is equal to the angle of reflection.
( Henced Proved)
Refraction of a Plane Wave

11. Time= Distance/Speed
T= MQ/C + QS/V
T= PQ sini/C + QR sinr/V
T= PQ sini/C + (PR-PQ)sinr/V

12. T= PQ(sini/C + sinr/V) + PR sinr/V
Position of Q is not fixed , time taken will not depend
upon term PQ
PQ(sini/C + sinr/V) = 0
But PQ is nor equal to zero
Sini/C + sinr/V
Sini/C = sinr/V
Sini/sinr = C/V=µ
Hence, snell’s law is proved
(Henced Proved)

13. 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

14. Thus sinic = B1B2/A1B2 = V1/V2 = n12
Where, 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.

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

16. Summary
According 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.

17. Thank-you