Huygen Wavefront: Drawing a Tangent to Wavelets

[gracy]

One rule of huygen theory isfollowing
The new wavefront is https://www.boundless.com/definition/tangent/ to the wavelets.

If we look at reflection,to draw new wavefront we should draw tangent to the wavelets.should the two blue wavelets touch each other?Cannot we draw tangent to these blue wavelets even when they are not touching each other to get the new wavefronts?

 

[gracy]

Cannot we draw tangent to these blue wavelets even when they are not touching each other to get the new wavefronts?

I am saying that

Is it right?The two wavelets are not touching each other at any point,so will the tangent give the new wavefront?

 

[sophiecentaur]

It's only the tangents for both /all wavelets that tell you where you get additive interference. If you take arbitrary tangents, the wavelets will not interfere constructively to form a wavefront. (Is that what was worrying you?)
It is only another statement of the Fermat Principle.

 

[gracy]

It's only the tangents for both /all wavelets that tell you where you get additive interference

Is my tangent(the tangent I have drawn in my picture)going to give me new wavefront?

 

[sophiecentaur]

Is my tangent(the tangent I have drawn in my picture)going to give me new wavefront?

How can it, if it does not end up in phase with all the others, from the other wavelets?
There is only one direction in which this happens.

 

[gracy]

How can it, if it does not end up in phase with all the others, from the other wavelets?

But in my animation ,tangent to only two wavelets is giving new wavefront.

 

[sophiecentaur]

But in my animation ,tangent to only two wavelets is giving new wavefront.

You have not shown two tangents, parallel to each other, in your diagram. If they are not parallel, then they will be sweeping in and out of phase as they travel outwards and there will be no wave formed. The only direction which a wave will form and be sustained is in the direction that the laws of reflection predict.
I had a similar problem to you, when I fought this thing initially (way back in history).

There is another point. If you show only two wavelets then you will not get cancellation in other directions - you will have a circular resultant wavefront with amplitude variation with angle (Young Slits idea). The reflection laws only give the maximum amplitude direction and ignore diffraction effects. i.e. it assumes a very wide reflector and ignores the effect of the restricted aperture.