A circular lens
Вставка
- Опубліковано 4 бер 2022
- This #short simulation shows the working of a lens made of a circular segment, that is, a disc cut by a straight line. It works here like the objective of a camera, by concentrating an incoming planar wave at the focal point of the lens. The index of refraction of the lens is equal to 2, so that according the the lensmaker's equation, see en.wikipedia.org/wiki/Lens#Le... the focal point should be at the center of the circle.
The color depends on the height (amplitude) of the wave, with white corresponding to the medium at rest. There are absorbing boundary conditions on the right border, and periodic boundary conditions at the top and bottom boundary of the displayed region.
For more optics simulations, see the playlist • Optics (refraction, di...
Render time: 9 minutes 20 seconds
Color scheme: Twilight by Bastian Bechtold
github.com/bastibe/twilight
Music: Lone Harvest by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 licence. creativecommons.org/licenses/...
Source: incompetech.com/music/royalty-...
Artist: incompetech.com/
See also images.math.cnrs.fr/Des-ondes... for more explanations (in French) on a few previous simulations of wave equations.
The simulation solves the wave equation by discretization. The algorithm is adapted from the paper hplgit.github.io/fdm-book/doc...
C code: github.com/nilsberglund-orlea...
www.idpoisson.fr/berglund/sof...
Many thanks to my colleague Marco Mancini for helping me to accelerate my code! - Наука та технологія
And this is why your grandpa's newspaper lens was so massive, LOL. I always loved playing with that thing.
This is helping me to slowly begin to understand optics.
If you really want to get into the subject and have your mind blown, then research Fourier transforms and how they're used in optics.
Stupidly useful and quite intuitive once it clicks.
Ah, the origin story of the villains of optics! (Those are the spherical aberrations...)
At least I think that one can already see the seeds of them in-between all the diffraction-effects.
Nice illustration but I have two concerns: The incoming plane wave diffracts at the top and bottom end of the lens, slightly disturbing the pattern in the process. Moreover, the lens size and focal length are still comparable to the wavelength and are hence far from an optical real world example (changing this would also fix my first concern). Therefore, I think another nice example would be to employ a Gaussian beam of shorter wavelength. Nevertheless, like your vids!
Thanks! Unfortunately, with the simulation method I use (finite differences), decreasing the wavelength would require increasing the resolution, which increases the render time. I can fix the diffraction issue at the extremities of the lens, though, by making the lens bigger. A forthcoming simulation will do that.
Amazing! I just wish it was a gradient of colors so we can see how the incoming light rays got flipped
I was just thinking, maybe the red band could go from yellow to red and the blue band could go from green to blue.
Thanks! Colors are related to wavelengths, so that is a bit tricky to simulate. It might be possible to use an oscillating source with a y-dependent frequency, but I'm not sure how it behaves with dispersion.
as far as I could tell it didn't yet reach a steady state here, as something inside the lens was still changing
Looking really neat though
That might also be rather close to the steady-state interference-pattern between all the internally reflected waves?
Thanks. There will be a forthcoming longer version, showing that the pattern at the end is not quite the steady state, but almost.
Wow! I love seeing the transition wavefronts. I see a vertical "Chirp" looking pattern across the lens. Very nice work! I'm a groupy!
Thank you very much!
This channel is so neat
Beautiful. I think you can even see the spherical aberration of the focus. Can you compare to an ellipsoid lens, which should be aberration free for light entering on the optical axis?
I can try that as well. There are a couple older simulations with ellipses on this channel, but they are in lower resolution.
Exceptional!
We can clearly see the spherical aberration in this one. Would have been better with some obstacle on top and bottom of the lens to suppress the diffraction at it's edges.
A forthcoming version will have a lens going all the way from top to bottom.
If "I don't know what's happening but it's very pretty" was a youtube channel.
Spherical and chromatic abberation, kinda like my brain before coffee.
Could you do a wave reflection off a *catenary* shaped mirror?
Ah yes, the brachistrochone lens.
I have a simulation with a hyperbolic mirror here: ua-cam.com/video/9VDU0FcgNLY/v-deo.html
Isn't the catenary a form of hyperbola? I'm not sure.
@@NilsBerglund A hyperbola, like parabolas and ellipses are conic sections, a catenary can look very similar to a parabola or hyperbola, but isn't a conic section. It would be interesting to see what kind of reflection/abberation a hanging cloth that forms a catenary would make! en.wikipedia.org/wiki/Catenary
I went: ”Hey, that’s not even a semi-circle!” Then I realised it’s probably a circular lens shown from the side…
It's the 2D equivalent of what you obtain when you cut a spherical ball with a plane.
Cool
I love the white in it and the twist off the side of the lens. Is that half a perfect circle? What happens when you put one beside it at different locations? Is there a way to show light from a light source at different spots 2D and 3D.
It's not exactly half a circle, a perfect circle has been cut by a straight line that does not pass through its center - the center of the circle is roughly where the waves are focused.
If you combine several lenses in a row, the distances between lenses have to be chosen in terms of the focal lengths to get a result that is interesting for optics.
If you drop some sand on a solid plate and vibrate the plate with a fixed frequency, you probably get similar patterns .
Indeed, these are commonly called Chladni figures.
@@NilsBerglund I saw some oobleck fluid videos in action lab channel. Any idea how to sim oobleck fluid?
These seem to be hard to simulate with wave-like partial differential equations alone. Wikipedia tells me that they "are better studied using tensor-valued constitutive equations, which are common in the field of continuum mechanics." So perhaps you need to simulate a 2d or 3d field of elastic deformations, with some particular deformation tensors.
@@NilsBerglund emm,, absolutely beyond me. But probably cool.
This could also be called a geodesic dome in an Electromagnetic pulse. Please could you do one with the Pyramid of Cheops shape , so we can see how solar microwaves etc can be focused to deliver a concentration of energy to a receiver in the basement. (as happened here).
In 2d, prism and pyramid would be triangles. Do you have a triangle in mind?
@@NilsBerglund Yes. I am imagining a triangular 'lens'. :-) I once saw a paper looking at electric fields from above being lensed under a massive pyramid and they definitely acted as a lens to create a focused region of high power under the pyramid.
stillnessinthestorm.com/2018/07/scientists-find-the-great-pyramid-of-giza-focuses-electromagnetic-energy/
The paper: aip.scitation.org/doi/pdf/10.1063/1.5026556
Unfortunately not a freely available paper.
this song is a banger
I wonder if this somewhat-particular (pun intended) pattern has any correlations to any Feynman Diagrams 🤔
Are these possibly in 3 dimensions? I know you'd still have to watch them on a screen, but with light and sound I think the differences by going up a D would be interesting
The main problem with 3D is the render time. With the method I use, it would take about 1000 times as long to make a 3D computation on a cube each side of which has 1000 grid points than in 2D.
@@NilsBerglund on the one hand I'm glad to know it's possible, on the other hand, *low whistle*
This is going to sound like a stupid question not what is but WHY is the seemingly repeating "fractal" pattern there? Especially horizontally.
Curious about what laws relate to the emergence of such patterns?????
The pattern is not truly fractal, because there is a lower limit to the wavelength. What you see may be due to resonance effects: waves trapped inside the lens or between the lens and the left boundary tend to form standing waves.
@@NilsBerglund Subbed. Can't wait for the next vid. Thanks!
It's fascinating what's going on at the front of the lens. From what I can tell it seems that some of waves must be bouncing off of the front of the lens and somehow influencing the incoming waves. Would waves bounce off of the left side of the screen?
That's the Fresnel reflection. It happens whenever a wave pass from a medium to another with a different index of refraction. The reflected waves do interact with the incoming waves, but don't alter them.
There is an imposed boundary condition at the left side. Idk if it causes reflection of waves. However there are periodic boundary conditions between the top and bottom, which help creating a standing wave.
Забавно, что свет на выходе не внутри конуса идёт, а почти внутри гиперболоида.
What music is this?
It is a track by Kevin MacLeod (who has contributed a *lot* of tracks to the YT audio library), you can find the details in the description here: ua-cam.com/video/g4Yh4GXJ7Vw/v-deo.html
@@NilsBerglund thank you!
Is it FDTD?
No, it is a bit simpler, because I only solve a the wave equation for a one-dimensional field. But I think the result is similar to what Maxwell's equations would give.
Source code for this? 🤯
See github.com/nilsberglund-orleans/UA-cam-simulations
I have not published the latest version of the code, but plan to do it soon.
@@NilsBerglund So this is an older version of the same code?
Yes indeed. I think that compared to the published code, in this one I just added the circular segment as a new shape.
@@NilsBerglund Next question... how long did this take to process on your rig?
It's written in the description: this one took 9 minutes and 20 seconds
Physics 'n' shyit