Name: Primary and Secondary Wavefront
Uploaded: 2019-07-19
Duration: 2 min 30 s
Description: The creation of wavefront causes a “chain reaction” of creating more wavefronts that pave the way for the propagation of waves. Let's dive deep into this phe...

Question

Derive the law of reflection using Huygen $'$ s Wave Theory.

Accepted Answer

According to Huygen $'$ s principle, each point of the wavefront is the source of a secondary disturbance and the wavelets emanating from these points spread out in all directions with the speed of the wave and if we draw a common tangent to all these spheres, we obtain the new position of the wavefront at a later time.

Let $XY$ be a plane reflecting surface and $AMB$ the incident plane wavefront. All the particles on $AB$ will be in vibrating in phase. Let $i$ be the angle of incidence and $r$ the angle of reflection. In the time $t$ , the disturbance at $A$ reaches $C$ , the secondary waves from the point $B$ must travel a distance $BD$ equal to $AC$ . With the point $B$ as centre and radius equal to $AC$ a sphere is constructed.

From the point $C$ , we draw tangents $CD$ and $CD'$ .

Then, $BD = BD'$ .

In $∆ BAC$ and $∆ BDC$ ,

$BC$ is common,

$BD = AC$ , and

$∠ BAC = ∠ BDC = 90 °$

$∴ ∆ B A C ≅ ∆ B D C$

and $∠ ABC = ∠ BCD$

But $∠ ABC = i and ∠ BCD = r$ , i.e., $i = r$ or the angle of incidence is equal to angle of reflection.

Since $AB, AD and XY$ are in the same plane. Therefore, the incident ray, reflected ray and normal at the point of incidence are all in the same plane. This is first law of reflection.

Derive the law of reflection using Huygen $'$ s Wave Theory.

Important Questions on Wave Nature of Light : Huygens' Principle

Learn and Prepare for any exam you want !

Derive the law of reflection using Huygen's Wave Theory.

Important Questions on Wave Nature of Light : Huygens' Principle

Learn and Prepare for any exam you want !

Derive the law of reflection using Huygen $'$ s Wave Theory.