Why Don't Spherical Waves Interfere: Exploring Huygens Principle

[alikazemi7]

Hi
according to Huygens principle every point on the wave front acts as a spherical source. so if a we emit monochromatic light on a screen without passing light from grating, we should see interference pattern but we don't. why don't these spherical waves interfere with each other? is this principle is valid when wave is passing through slits?

 

[Chandra Prayaga]

The purpose of Huygen's principle is to start from a wavefront and from that, construct the next (a little later) wavefront. The spherical wavefronts from each point source do interfere (add) with each other, and result in the next wavefront.

 

[alikazemi7]

The purpose of Huygen's principle is to start from a wavefront and from that, construct the next (a little later) wavefront. The spherical wavefronts from each point source do interfere (add) with each other, and result in the next wavefront.

so according to what principles we see interference patterns when a wave pass through a slit or grating?

 

[Garlic]

In order interference pattern to show up, you will need two (or more) light sources with the same wavelength so that they interfere with each other. If you have a single light source, it doesn't interfere with itself. When the wave passes through a slit or grating, (huygens principle) there is two light sources, and because the light comes from the same source, both of them has the same wavelength, so they interfere and therefore you see an interference pattern.

 

[alikazemi7]

In order interference pattern to show up, you will need two (or more) light sources with the same wavelength so that they interfere with each other. If you have a single light source, it doesn't interfere with itself. When the wave passes through a slit or grating, (huygens principle) there is two light sources, and because the light comes from the same source, both of them has the same wavelength, so they interfere and therefore you see an interference pattern.

but in diffraction phenomenon in which we have a single slit and of course one source, the wave interfere with itself and we see interference pattern.

 

[Garlic]

but in diffraction phenomenon in which we have a single slit and of course one source, the wave interfere with itself and we see interference pattern.

I'm really sorry, the single slit diffraction wasn't teached to us, I diddn't know it.
I've searched it and found some links that can help you:
http://physics.stackexchange.com/qu...t-diffraction-produce-an-interference-pattern
and https://en.wikipedia.org/wiki/Huygens–Fresnel_principle

 

[Chandra Prayaga]

In a single slit, different points along the width of the slit act as point sources and emit spherical wavefronts. Again, subsequent wavefronts can be constructed using the Huygens principle. These waves do interfere on the screen and produce the interference (or diffraction) pattern.

 

[alikazemi7]

In a single slit, different points along the width of the slit act as point sources and emit spherical wavefronts. Again, subsequent wavefronts can be constructed using the Huygens principle. These waves do interfere on the screen and produce the interference (or diffraction) pattern.

this is my question: when monochromatic light emits on a screen without passing from a slit/slits we don't see interference patterns. why the spherical waves on the wave front don't interfere with each other in this situation?

 

[Chandra Prayaga]

They do interfere. What happens is exactly what happens if you start widening the slit. More spherical waves with a complete range of phase differences are interfering, giving an overall uniform illumination.

 

[Marcis Rancans]

What do you mean by

complete range of phase

?

 

[Chandra Prayaga]

What do you mean by ?

So, if monochromatic light hits a screen directly, you are using Huygens principle to construct successive wavefronts. The envelope of the spherical waves from individual point sources keeps producing the next wavefront of the same shape, and when the last wavefront hits the screen, every point on the screen is hit by the same state of the wave, and therefore shows the same intensity. This is seen easiest for plane wavefronts, and you just replace one of the wavefronts with a screen.

We should note that the Huygens principle is used to construct wavefronts, and not interference (or diffraction) patterns. These patterns are explained by the Huygens-Fresnel principle, and the use of it for a single slit diffraction pattern (Fraunhoffer). This takes into account the phase differences of spherical waves emitted by different points along the width of the slit, and interfering on the screen. I doubt if this part can be described without actual calculations, which are given in any book on optics.

 

[vanhees71]

First of all to see interference effects through diffraction you need a coherent (or at least partially coherent) light source. If you use, e.g., thermal light, you have light waves emitted from a lot of spots which have totally uncorrelated phases, and thus the light is completely incoherent. It thus cannot interfere, and thus just the intensities add (this is however only approximately true; in principle there's also interference in such cases; see the Hanbury-Brown and Twiss effect).

Second, one should be aware that Huygens's principle is very heuristic and valid only in odd space dimensions (so it's in fact valid in the usual 3D space), but that's another story.

The full theory of diffraction is quite complicated. Have a look in a good textbook on optics, e.g., Born and Wolf or (a bit more compact) Sommerfeld Lectures vol. IV.

 

[just dani ok]

What if we use a laser beam whose diameter is smaller than the width of single slit. Will we see light and dark pattern on the screen when the beam only hit one edge of the slit? what if the laser beam goes through between the edges of the slit, without hitting them?

 

[nasu]

this is my question: when monochromatic light emits on a screen without passing from a slit/slits we don't see interference patterns. why the spherical waves on the wave front don't interfere with each other in this situation?

The problem is that you consider "interference pattern" only the alternation of maxima and minima.
What you see on a screen without any slit or grating it is the result of interference (or can be considered to be) of the waves produced by these secondary sources. The "pattern" is a uniform distribution of light intensity. Maybe decreasing smoothly from center to the edge.
When you put something in the path you simply cut off some of the previously interfering waves so the pattern will change from the uniform to something else.

 

[jtbell]

What if we use a laser beam whose diameter is smaller than the width of single slit. Will we see light and dark pattern on the screen when the beam only hit one edge of the slit?

In that case we have edge diffraction:

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/bardif.html
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/difopa.html

what if the laser beam goes through between the edges of the slit, without hitting them?

In that case we get no diffraction.

 

[just dani ok]

In that case we have edge diffraction:
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/bardif.html
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/difopa.html

Are the solutions derived from Huygen's principle?
The pattern shown in the first link only occur when the laser is spread eg. by lens, but when the laser beam is not spread, the pattern doesn't occur.

The formula often used to derive single slit diffraction implies that the source of interference pattern is the space in the slit, as shown in this video

which should be still applicable in the case of small diameter laser beam without hitting the edge of the slit.

 

[just dani ok]

additional evidence that the diffraction effect originated from the edge of the obstacle. Shine a laser beam on a single slit diffraction with vertical slit orientation. You get usual single slit diffraction pattern.
Then tilt the slit by making its top side closer to the screen. Now the pattern becomes circular, whose center located on the elongation of the slit.

 

[tech99]

additional evidence that the diffraction effect originated from the edge of the obstacle. Shine a laser beam on a single slit diffraction with vertical slit orientation. You get usual single slit diffraction pattern.
Then tilt the slit by making its top side closer to the screen. Now the pattern becomes circular, whose center located on the elongation of the slit.

Huygens wavelets are not proven to exist so far as I am aware, but are a means of obtaining the correct answer. There is an anomaly with the theory that the radiation from the Huygens Source has to be assumed to radiate only forwards with a cosine shaped lobe, and this is incompatible with a very small source. Whenever a wavefront is curtailed in any way, by cutting off the edges for instance, or by an obstruction, there is diffraction.

 

[just dani ok]

Huygens wavelets are not proven to exist so far as I am aware, but are a means of obtaining the correct answer. There is an anomaly with the theory that the radiation from the Huygens Source has to be assumed to radiate only forwards with a cosine shaped lobe, and this is incompatible with a very small source. Whenever a wavefront is curtailed in any way, by cutting off the edges for instance, or by an obstruction, there is diffraction.

Have you ever heard about non-diffractive obstacle or non-diffractive slit?