Question

Define the term wavefront. Using Huygens wave theory, verify the law of reflection.

Answer 1

When a light source emits light, all the particles around the light begin to vibrate. A wavefront is continuous locus of all such particles, which are vibrating in the same phase.

Laws of reflection using Huygens principle: Huygens principle states that

(i) each point on the primary wavefront acts as a fresh source of new disturbance called secondary wavelets, which sends disturbance in all directions with velocity of light. 

(ii) at any instant, a surface touching these secondary wavelets in forward direction gives the new position of the wavefront at that instant called the secondary wavefront.

Consider following figure:

• M₁M₂ is a plane mirror.

 • AB is plane wavefront incident on M₁M₂ at angle of incidence i.

• According to Huygens principle, every point on AB is source of secondary wavelets.

 • Suppose wavelets from B reach M₁M₂ on point A′ in t seconds. 

• Wavelets from A will reach point B′ in t seconds and wavelets from D reach D′ in t seconds. 

• If velocity of light is c, then the time t taken by the wavelets to go from D to D′ will be

t = DP/C + PD/C ... (1)

Now, from the right-angled triangle ADP, we get

∠ DAP = i ⇒ DP = AP Sin i

and from the right-angled triangle PD 'A ', we get

∠A' D' P' = r ⇒ PD' = A' P Sin r

Substituting the value of DP and PD′ in Eq. (1), we get

Now,

AA' = AP' + PA' ⇒ PA' = AA' - AP

Therefore,

Now, we know that the wavelets from different points on a wavefront will take some time to reach the corresponding point on the reflected wavefront; thus, the time t should be independent of AP. Therefore,

Thus, the angle of incidence is equal to the angle of reflection. Also, the incident wavefront AB, the reflected wavefront A′B′ and the normal, all lie in the same plane. These are the two laws of reflection that have been verified using Huygens principle.