explain the Huygens principle with example?
Huygens principle states that every point on a wave front acts as a secondary source and is capable of giving out waves in all directions. the envelope of this waves gives the next wavefront reaching in time t+dt
A) spherical wave front:
a wave front comming from source S reaches in time t consider 3 pts.X Y and Z which act as secondary sources. acc to huygene.
with x, y and z as centers draw circles of radius c x dt because velocity , c = distance divide by time
envelope of this gives a new wave front that reaches in additional time t + dt.
B) similarly plane wave front is another example.with same explanation..with the exception of its definition that is:
it is a small part of a spherical wave front comming from a distant source.
P.s only consider the first two images the third one is inteference,
hope my answer helps..
Huygens’ Principle is based on the following assumptions:
Each point on the primary wavefront acts as a source of secondary wavelets, sending out disturbance in all directions in a similar manner as the original source of light does.
The new position of the wavefront at any instant (called secondary wave front) is the envelope of the secondary wavelets at that instant.
Laws of Reflection on Wave Theory
Consider any point Q on the incident wavefront PA.
When the disturbance from P on incident wavefront reaches point , the disturbance from point Q reaches .
If c is velocity of light, then time taken by light to go from point Q to (via point K) is given by,
In right-angled ΔAQK,
∠QAK = i
∴ QK = AK sin i
In right-angled ,
Substituting these values in equation (1),
The rays from different points on incident wavefront will take the same time to reach the corresponding points on the reflected wavefront, if ‘t’ given by equation (ii) is independent of AK.
∴ AK (sin i − sin r) = 0
sin i − sin r = 0
sin i = sin r
i = r
i.e., the angle of incidence is equal to the angle of reflection.
Also, the incident ray (LA or), reflected ray (or ), and the normal (AN) − all lie in the same plane.
Refraction On The Basis Of Wave Theory
Consider any point Q on the incident wavefront.
Suppose when disturbance from point P on incident wavefront reaches point on the refracted wavefront, the disturbance from point Q reaches on the refracting surface XY.
Since represents the refracted wavefront, the time taken by light to travel from a point on incident wavefront to the corresponding point on refracted wavefront should always be the same. Now, time taken by light to go from Q to will be
In right-angled ΔAQK, ∠QAK = i
∴ QK = AK sin i … (ii)
Substituting (ii) and (iii) in equation (i),
The rays from different points on the incident wavefront will take the same time to reach the corresponding points on the refracted wavefront i.e., t given by equation (iv) is independent of AK. It will happen so, if
This is the Snell’s law for refraction of light.
2.secondary wavelet travel in a medium in a all directions with the speed of original wave.
3.envelope of secondary wavelet in forward direction gives the new wave front at that instant.