The Huygens–Fresnel principle

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In summary: Then you're all set.In summary, the conversation discusses the concept of constructive interference and its relation to the Huygens-Fresnel principle and the interference pattern of a double slit. The question posed is about the direction in which regions of constructive interference travel, and the answer is determined by finding the point where the crests of the incident and reflected waves overlap. The correct answer is point c, and the direction of constructive interference is determined by the propagation of waves from this point.
  • #1
Hamal_Arietis
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Homework Statement


3229193775_1519209300_574_574.jpg

I don't understand about some words of this problem. Does "over time" mean? Why constructive interference (CI) appear?

Homework Equations


I think we use The Huygens–Fresnel principle

The Attempt at a Solution


I choose answer 3-c
3229194544_1358055013_574_574.jpg

But I don't know the physical phenomenon.
 
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  • #2
The incident wave and reflected wave interferes with each other and produces regions (crests) of inteference that travels in a certain direction.
The question wants you to answer in which direction these constructive interference regions would travel.
 
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  • #3
What is the correct answer?
 
  • #4
Have a look at the concept of reflection in a mirror and combine this with what you know about the interference pattern of a double slit.
 
  • #5
The correct answer is 1-a.
andrevdh said:
what you know about the interference pattern of a double slit.
There are many double slits not one . And the interference image is total of many double slits. How to know the direction of interference?
 
  • #6
Help me ? Thanks
 
  • #7
Do any of the marked points below represent a point of constructive interference between the incident and reflected waves? If so, which?
upload_2016-10-28_16-30-37.png
 
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  • #8
I think a, b and c. because they are in constructive interference area between the incident and reflected waves.
 
  • #9
If I seem the souce S is very far from wall. The constructive interference area between the incident and reflected waves will be rectilineal. And I take the S' image, we have a double slits SS'. The waves go to P before going to Q. So 1-a is the right direction. Is OK ?
3229243376_204113474_574_574.jpg
 
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  • #10
Hamal_Arietis said:
I think a, b and c. because they are in constructive interference area between the incident and reflected waves.
The question asks about crests of constructive interference. In post #7 I should have been more specific and asked which of the 4 points is located on a crest of constructive interference. Only one of the points a, b, c, d is such a point.
 
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  • #11
i think it is b. I don't know how the constructive interference appears? Because if constructive interference appears. Must have double slits or d2-d1=k lambda. I don't see any double slits. And can't calculate d2-d1. Does my idea in #9 correct?
 
  • #12
Interference occurs whenever two or more waves overlap. The double slit experiment is just one example of a case where waves interfere. In the situation that you are dealing with here, the reflected waves overlap with the incoming waves. So, they will interfere.

A crest of constructive interference occurs where the crest of one wave overlaps the crest of another wave. So, if you look at the point a, b, c, d in post #7, only one of those points is a place where the crest of an incoming wave overlaps the crest of a reflected wave. (The blue lines represent wave crests.)
 
  • #13
TSny said:
Interference occurs whenever two or more waves overlap. The double slit experiment is just one example of a case where waves interfere. In the situation that you are dealing with here, the reflected waves overlap with the incoming waves. So, they will interfere.

A crest of constructive interference occurs where the crest of one wave overlaps the crest of another wave. So, if you look at the point a, b, c, d in post #7, only one of those points is a place where the crest of an incoming wave overlaps the crest of a reflected wave. (The blue lines represent wave crests.)
Is c right ?Intially I think your blue lines is the direction of the incident. so I choose b
 
  • #14
upload_2016-10-29_11-43-15.png

The blues lines are the wave crests. The lighter blue lines are wave crests of the incident wave. The green arrows show the direction of propagation of these incident wave crests. The darker blue lines are wave crests of the reflected wave. The orange arrows show the direction of propagation of these reflected wave crests.

At which of the points a b c d does a wave crest of the incident wave overlap with a wave crest of the reflected wave?
 

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  • #15
I think that is c. But how this connect with the direction of constructive interference appear ?
 
  • #16
upload_2016-10-30_0-0-4.png

The red points will be the crest of the incident wave overlap with a wave crest of the reflected wave.
 

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  • #17
Hamal_Arietis said:
I think that is c. But how this connect with the direction of constructive interference appear ?
Yes, point c is a point where crests are constructively interfering. You want to find the direction in which point c moves as the waves propagate. Draw the figure as shown. On the same figure, draw the waves as they would appear a little later in time.
 
  • #18
I understanded. Thanks
upload_2016-10-30_0-9-50.png
 
  • #19
OK. Good.
 

What is the Huygens-Fresnel principle?

The Huygens-Fresnel principle is a fundamental concept in wave optics that explains the behavior of light as it propagates through a medium. It states that every point on a wave front can be considered as a source of secondary wavelets, and the sum of these secondary wavelets determines the shape and direction of the new wave front.

Who developed the Huygens-Fresnel principle?

The principle was first proposed by Dutch physicist Christiaan Huygens in the late 17th century, and later refined by French physicist Augustin-Jean Fresnel in the early 19th century.

What is the significance of the Huygens-Fresnel principle?

The Huygens-Fresnel principle is a key concept in understanding the behavior of light and other waves in various mediums. It provides a mathematical framework for predicting how waves will propagate and interact with obstacles, and has many practical applications in fields such as optics, acoustics, and electromagnetism.

How does the Huygens-Fresnel principle relate to diffraction and interference?

The Huygens-Fresnel principle can be used to explain the phenomena of diffraction and interference, which are important in understanding the behavior of light and other waves. Diffraction occurs when a wave passes through an opening or around an obstacle, causing it to spread out and create a diffraction pattern. Interference occurs when two or more waves overlap and either reinforce or cancel each other out. The Huygens-Fresnel principle can be used to mathematically predict the patterns created by these phenomena.

Are there any limitations to the Huygens-Fresnel principle?

While the Huygens-Fresnel principle is a powerful tool for understanding the behavior of waves, it does have some limitations. It is based on certain assumptions, such as the wave nature of light and the absence of absorption, which may not always hold true in real-world situations. Additionally, the principle is most accurate for waves with small amplitudes and in homogeneous mediums, and may not accurately predict the behavior of waves in more complex systems.

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