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On the Lighter Side => New Theories => Topic started by: hamdani yusuf on 11/04/2021 05:36:10

Title: Is there a better explanation for interference pattern produced in single slit
Post by: hamdani yusuf on 11/04/2021 05:36:10
Single slit experiment is usually explained using Huygen's principle,  like in these videos.



Is it really the best explanation we can provide?

Title: Re: Is there a better explanation for interference pattern produced in single slit
Post by: hamdani yusuf on 11/04/2021 07:29:19
The explanation above produces predictions which are contrary to some experimental results.
Let's focus on the central point of the screen. According to Huygen's principle, integrating the wavelets from all points between the edges of the slit should produce bright spot or dark spot on the centre of the screen, depending on the width of the slit. But the video of experiment using adjustable slit width shows that screen center is always bright at various width.
Title: Re: Is there a better explanation for interference pattern produced in single slit
Post by: CrazyScientist on 11/04/2021 07:36:49
There's for example a model known as Pilot-Wave Hydrodynamics:
https://fyfluiddynamics.com/2018/01/this-post-is-part-of-a-collaborative-series-with-2/

(https://i2.wp.com/fyfluiddynamics.com/wp-content/uploads/2018/01/tumblr_p1zxatFaDG1qckzoqo1_400.gif?fit=350%2C320&ssl=1)
Title: Re: Is there a better explanation for interference pattern produced in single slit
Post by: hamdani yusuf on 11/04/2021 10:44:02
There's for example a model known as Pilot-Wave Hydrodynamics:
https://fyfluiddynamics.com/2018/01/this-post-is-part-of-a-collaborative-series-with-2/
The link doesn't provide an explanation. It just shows an analogy instead. It doesn't show how the results can be derived from some basic principles.
Quote
When a walker passes through a single-slit (top row), it’s deflected in a seemingly random direction due to its waves interacting with the slit. But if you watch enough walkers traverse the slit, you can put together a statistical representation of where the walker will get deflected. Compare that with the results for a series of photons passing through a slit one-at-a-time, and you’ll see a remarkable match-up.
Title: Re: Is there a better explanation for interference pattern produced in single slit
Post by: hamdani yusuf on 16/04/2021 11:55:18
Explanation below is commonly used to explain single slit diffraction-interference pattern.
https://courses.lumenlearning.com/austincc-physics2/chapter/27-5-single-slit-diffraction/
(https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/222/2014/12/20111429/Figure_28_05_01a.jpg)
Quote
Light passing through a single slit forms a diffraction pattern somewhat different from those formed by double slits or diffraction gratings. Figure 1 shows a single slit diffraction pattern. Note that the central maximum is larger than those on either side, and that the intensity decreases rapidly on either side. In contrast, a diffraction grating produces evenly spaced lines that dim slowly on either side of center.

(https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/222/2014/12/20111430/Figure_28_05_02a.jpg)
Quote
The analysis of single slit diffraction is illustrated in Figure 2. Here we consider light coming from different parts of the same slit. According to Huygens’s principle, every part of the wavefront in the slit emits wavelets. These are like rays that start out in phase and head in all directions. (Each ray is perpendicular to the wavefront of a wavelet.) Assuming the screen is very far away compared with the size of the slit, rays heading toward a common destination are nearly parallel. When they travel straight ahead, as in Figure 2a, they remain in phase, and a central maximum is obtained. However, when rays travel at an angle θ relative to the original direction of the beam, each travels a different distance to a common location, and they can arrive in or out of phase. In Figure 2b, the ray from the bottom travels a distance of one wavelength λ farther than the ray from the top. Thus a ray from the center travels a distance λ/2 farther than the one on the left, arrives out of phase, and interferes destructively. A ray from slightly above the center and one from slightly above the bottom will also cancel one another. In fact, each ray from the slit will have another to interfere destructively, and a minimum in intensity will occur at this angle. There will be another minimum at the same angle to the right of the incident direction of the light.

(https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/222/2014/12/20111432/Figure_28_05_03a.jpg)
Quote
At the larger angle shown in Figure 2c, the path lengths differ by  3λ/2 for rays from the top and bottom of the slit. One ray travels a distance λ different from the ray from the bottom and arrives in phase, interfering constructively. Two rays, each from slightly above those two, will also add constructively. Most rays from the slit will have another to interfere with constructively, and a maximum in intensity will occur at this angle. However, all rays do not interfere constructively for this situation, and so the maximum is not as intense as the central maximum. Finally, in Figure 2d, the angle shown is large enough to produce a second minimum. As seen in the figure, the difference in path length for rays from either side of the slit is D sin θ, and we see that a destructive minimum is obtained when this distance is an integral multiple of the wavelength.

Thus, to obtain destructive interference for a single slit, D sin θ = mλ, for m = 1,−1,2,−2,3, . . . (destructive), where D is the slit width, λ is the light’s wavelength, θ is the angle relative to the original direction of the light, and m is the order of the minimum. Figure 3 shows a graph of intensity for single slit interference, and it is apparent that the maxima on either side of the central maximum are much less intense and not as wide.
Title: Re: Is there a better explanation for interference pattern produced in single slit
Post by: hamdani yusuf on 17/04/2021 22:43:52
Quote
You never change things by fighting the existing reality.
To change something, build a new model that makes the existing model obsolete.
Buckminster Fuller
Title: Re: Is there a better explanation for interference pattern produced in single slit
Post by: hamdani yusuf on 23/04/2021 23:19:01
By adding a lens in front of the slit, we can get different results. Now it's possible to produce dark fringe in the middle of the screen.