By the way, I was wondering what could happen if there were, say, two places where the lens had a peak in refractive index? More peaks ? Though tht would make n a function of r and θ as in polar coordinates, else I think that wouldn't be possible? Another idea : absolute value of a tangent function? How about just the absolute value of r? Probably not very interesting cases, but thereyago.
I just found out about 3blue1brown the other day, we are not too far apart. As far as the lens is concerned, r can not go negative, so the abs(r) may not be too interesting. I don't remember if we tried the tangent or not. I am fairly certain that if we saw two peaks, light would be attracted to both peaks and you would see the rays moving towards whichever is closest. I am not sure, though. Definitely something to try!
It's all available on github (it's not the cleanest, but it uses c++ and cairo): github.com/leios/simuleios/tree/master/geometrical_optics It's basically following the vector form of snell's law in a time-dependent manner by taking into account the changing velocity of light.
"basically just glass" no, because the edges are not straight and parallel. You appear to have a constant IOR as the rays pass through the bulk, since they are straight lines. But the IOR at the point where the ray enters must be just right to match the angle of the ray's intersection with the edge, which varies continuously since the profile varies.
Even if we can't get a refractive index higher than 36, I'd still like to see what that lens looks like up to 36. Either have a core of 36 for all r where the intended index is higher than 36, or shrink it so only the center point is 36.
I suspect the math itself might be similar. After all infinite refractive index = lightspeed reduced to zero. Which in a sense is what happens to light falling inside a black hole, from the point of view of an outside observer.
No, they follow very different equations :) Black Holes capture stuff because of immense gravitational pull caused by their immense mass, and the lense captures light because it follows the fermat principle, which basically makes light bend towards greater refractive indexes
This is a great video. I’ve been a lens designer for 44 years and I developed a large scale gradient index glass known as GRADIUM in the early 90’s. I’ve played around with different gradient geometries but have never seen a video simulation like in this video. What software were you using and how did you make it look like real time ray tracing while varying the parameters? Really cool. Good job. Please get back to me. I’d like to discuss gradients with you and tell you about some of the new 3D glass printing we are doing (including gradient index glass) Thanks, Paul
I actually developed the code myself. It was written in Cairo (C++ library). Each visual took a super long time, but if you want to replicate it, I would probably just do raytracing like normal and then after the light ray intersects with the object, switch to a timestepping scheme where you move the light forward by some dt every step and use the new refractive index at the new location to figure out how light bends. I thought about doing a full 3D visualization, but honestly didn't want to model a 3D environment and showing the rays in this way is actually more clear to the viewers.
If you want a nice lens concept, try the Cloaking Lens: take the "Invisble lens" concept, but make it so the refractive index diverges before reaching the center (before radius r= 0, at r=k), that way you perhaps you'd be able to put an object in the middle with light going around it and leaving in the same direction?
I need to think about what the equation would look like for that one. My fear is that the rays entering the lens with a position of x < k (measured from the origin), will not be "invisible" and will instead hit the object.
What does the effect of an equation with a singularity outside the origin look like? a simple example would be (R-k)/(r-k). Indeed at least one ray must hit the singularity, even in the invisible lens case (the central ray). Actually looking at the inv. lens paper, what if you replace every instance of a/r (or R/r) in the n(r) formula for (R-k)/(r-k)?
just tried it, all the rays enter and move towards the assigned value for k, at which point, the refractive index is way too high and the rays cease to move. I suppose we could gloss over that by forcing the index to remain under a certain value, though.
Oh interesting! Looks like a cool problem :) I'm thinking the solution might be diverging the rays before hitting the singularity? (so maybe a ring of index
I just used g++, but I used Cairo for the visualization, so you will need to load that. As a side note, the reason I want to redo this is because Cairo is a vector-drawing library, which means that it draws an image at a time and outputs it to file before mving onto the next image. This is prohibitively slow and meant that in order to create videos, I would need to create a huge number of images and string them together at 60 fps.
LeiosOS well, aren’t you recording the video in real time , like simulating it using the code , why do you need to produce many different images , can’t the same thing be achieved with code , like , if we consider a point at the tip of the moving light Ray , which leaves its trace as it moves , we would just need move/trigger that point into a certain direction from the origin and it will just trace(color) the desired Ray path, is there any problem in this approach, maybe it won’t generalise ! Or will it?
I'd like to make some kind of real-time raytraced simulation to experience in VR. That's probably as close to 'experiencing' theoretical optics as we can get. It would be fun to add some lasers and other various visible light emitters, with some prisms and mirrors and everything else to setup a 'table' for experimenting on.
Light doesnt literally move slower. It just takes longer to move through the material, due to more particles getting in the lights way, so it has to bounce more.
That's one way to look at it. But regardless, the net effect is the same. Right? Light "slows down" in a lens and we use the difference in velocity to measure the index of refraction
This is so awesome. I'm a CS student at communtiy college and I'd love to see a video on how you made the code for this animation. Maybe even explaining some of the physics concepts like Snell's law and showing how you implemented it into code. I'm a huge fan of your work please keep these videos up I assure you you are inspiring many young thinkers!
The beautiful part about the last one is that the very small entering index would unsure a very dimm reflection. However, I think it's should be noted that shape has to be spherical for that specific gradient to work. It would be really interesting to find the invisibility index grading for a non trivial shape in that program.
LeiosOS oh, I meant that I would like to see what the strength map of the refractive index for a non-spherical arbitrary shape would be. For example a concave polygon, would it even be possible to be made invisible?
I bet Renderman or Vray could show what it would actually look like. I use Renderman, if the refractive index is constant throughout the sphere I could probably recreate it if I knew what to input into the material settings.
wait, recreate what what would actually look like? Do you mean for full 3d visualizations? For each of the unusual lenses, the refractive index varied on the inside of the lens, so it'll be hard to implement, but certainly not impossible!
Just a minor correct, the light doesnt actually slow down when it hits the medium, It just travels a further distance through it giving the resultant effect of slower without actually slowing
Wait, is that true? I always thought the refractive index was defined by the change in speed as light enters different media: math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html (first couple of paragraphs)
I watched this in 2018 and was looking for Information of this kind for about 25 years. very interesting, maybe some of these lenses will be made in the future.
The lens at 1:36 (96 s) though seems like it would approximate a black hole in some ways, because a black hole bends all the light that falls on it into itself and absorbs it completely - and this effect is, after all, called "gravitational lensing". Granted, the _speed_ of the light doesn't change, but the point is that it can affect the _geometry_ of the rays in a similar fashion, and thus there _is_ a natural analogue, if perhaps not exact, for this case. If you were looking at this lens, it would look like a black circle, which is the same way the horizon of a black hole would appear to you. For the other lenses, while they may not be real-life realizable, it'd be great to see them realized virtually in a computer raytracing simulation, so we could see what it'd actually look like to look through them, _were_ they to be able to exist. I wonder if POV-Ray or similar computer graphics software could be used to achieve this. Really would be interested in seeing what it'd look like to look through the lens at 2:24 (144 s).
We had to develop a specific time-dependent raytracing method for these lenses so we could more accurately trace the light as it moved through the lens. I feel there is definitely a way to work with these in other software, but I am not sure...
For a lens, i'd love to see solutions to differential equations for the function. Maybe like a solution to the logistic equation or something similar. I wouldn't be surprised if you could draw some sort of real world conclusions from it too with a bit more work.
That's very interesting! if I'm understanding correctly at least related to an idea I had you could use it to focus a magnetic field to a fine point using something like a lense. basically creating a focused magnetic field using a laser instead of magnets. you made it easier to visualize thanks!
For better visualisation, you might want to colour the rays of light in a gradient from top to bottom (of input). That way, instead of just seeing that rays end up somewhere, you see at a glance /which/ rays end up where. This would be especially useful when sweeping through a range of values. It would give you more of an idea of the image on the other side. Obviously it's now a while since this video was made, and I haven't checked to see if this project is still active, but I thought I'd share the idea!
I had more in mind changing the formulas of the force of Gravity For instance, how would an orbit look like if the force of Gravity was depended not on the Distance squared, but the Log of both distance time pi or perhaps other formula I can't think about due to my limited knowledges of maths Basically, exploring similar concept as you did with the lenses
I have a question. From what I understand, the slower speed of light in a dense medium is not due to the individual photons slowing down. Each photon still moves at C, no matter what. Light appears to slow because the photons take a more meandering path when there's a bunch of mass in the way. So my question is this: why do all the photons end up in the same trajectory if they're each following different meandering paths?
For the approximation we are taking here, it's not obvious that the light is taking a "meandering path." We kinda just ignored it for this. It's a lot easier to think of this when you think of light as a wave, not a particle... but even that is unclear until you start talking about individual atoms and such. I think this gave a decent description of the phenomenon: physics.stackexchange.com/questions/105573/why-does-the-light-travel-slower-in-denser-medium
The first impossible lens could be the exact reason on why light can’t escape the black hole since if times the gravitational pull by the index it could lead to mass and/ or density.
i'm pretty sure light only bends going from one medium to the next but in your case light is continuously bending as it travels through the lens. Also if you're going to do theoretical lenses, what about a negative index of refraction ;)
Light is continually bending because we chose a continuously varying function inside the lens. Also, I didn't know how to interpret negative indices... but that might be a good thing to try!
I see how you could have done a simple check when it entered a lense to change the angle. How did you change the angle gradually or curve when it was inside? You said it is vector graphics, so you calculated it every pixel or what?
I thought it might be interesting to use refractive indexes as a complex function visualisation. `C (x,y) -> C (z,Index)`. What do you think this might look like for some hard to visualise complex functions?
I have an invisible lens in my house, actually! Most people that come over don't call it that though, they call it by some odd, alien term known as "glass"
Ooo... I tried to think about it way back in maybe 2012 or 2013 so I was very young and not sure how much what I'm about to say is right but I was very confident about what I did then... What I found out that if you define these functions of refractive index as a function of position and if you precisely know the momentum of photon you're about to shine then Heisenberg's Uncertainty principle should kick in and ruin everything you're trying to do because by knowing the refractive index and initial momentum, you can figure out the final momentum so if you're certain about initial momentum then you can be certain about the final momentum or in this case the momentum at a perticular position but now according to uncertainty principle you cannot be certain about momentum and position simultaneously and defining refractive index as a function of position exactly does that... So all these lenses are impossible lenses which have their refractive index defined as a function of position...
WTF you serious? Light is not moving slower at all, light is always traveling at lightspeed! It just takes a longer way which needs more time to travel.
Is a lens possible, in which there would be a preferred direction/helicity of light rays/that 'twists' light? I mean not the polarization, but in the handedness in which the rays swirl around the center. That way, we could not only model a Schwarzschild blackholes causal structure bellow its horizon, but also the frame dragging/lensing of a Kerr black hole.
Roel Lemaire Actually we can assimilate the bending of spacetime with a "void refraction index", and the effect is mathematically accurate ! Such an index would depend on the angle of incidence Theta and the distance from the black hole R : n ~ 1 + (GM/Rc)*(1 + cos(Theta)^2)
We could probably do that. We had to do some tricks to get the ray-tracing to work here, but we could do that with a much larger number of rays to get a similar effect.
Unless the light is perpendicular to the pane of glass, the light will be shifted to the side by an amount proportional to the thickness of the glass. The "invisible lens" doesn't cause the light be shifted.
Like the lens that has an infinite index of refraction at the origin, how about a lens that makes incident light always travel tangent to the radius such that it perpetually orbits the origin?
Be neat to put some of these through 3d software...though hopefully not blow the cpu up with div/0 stuff. The second one, isn't that a black hole due to extreme gravity capturing the light? Really neat vid!
Yeah. A lot of people have wanted to do this. I think part of the problem here was that we used a special method to do this simulation that was "time-dependent" so normal raytracing methods would break down at some point.
The light source of these experiments were all parallel, as if the lighsource was infinitely far away. How would the light rays travel through the "invisible lens" if the point of origin was, say, 1 diameter of the circle away?
Ultimately, this would cause a lot of scattering, but because it's a spherical lens, there wouldn't be too much that changes with the actual raytracing here.
Now I'm wondering what happens if you do the double slit experiment behind the invisible lens. Do you get a different result than without the lens if both the slits are behind the lens/only one slit is behind the lens?
Thanks for bringing this to my attention! I've added a link that is not behind a paywall in the description. Here is is again: iopscience.iop.org/article/10.1088/1367-2630/13/8/083007
We might pick up something like this again soon, except for the wave nature of light. In fact, there is still a good bit left to do with ray optics. Let me know if you have any ideas!
I guess infinite refractive index cam be seen in nature. It could be at the singularity point in the black hole where it has 0 volume and infinite density. So maybe it can be said that the singularity point is the brightest? I dunno. Just guessing
Sure thing! The cloak is two concentric cylinders, inner radius a, outer radius b Anything within the inner radius is cloaked, so index doesn't matter. The lens part, between a and b, has anisotropic permittivity and permeability, defined in cylindrical coordinate directions, namely: ε_r = μ_r = (r - a)/r ε_θ = μ_θ = r/(r-a) ε_z = μ_z = (b/(b-a))**2 * (r-a)/r (science.sciencemag.org/content/314/5801/977/tab-pdf paywalled)
Well,but how does the speed of light inside any lense reduce without breaking s. relativity theory?why do we still use refractive index=c/v when relativity says the for an arbitrary observer speed of a photon remains constant ?
I would also like to add in wave-particle duality. While the wave will slow down, the particle part is still traveling at C. It's just not taking the fastest route possible. So, it is both slowing down and staying at the same speed. It just depends on if you want to talk about light as a particle or a wave. (By the way, I am just a high school student who watches a lot of educational TH-cam, so if you really care about knowing the answer, google will probably be a better friend than I).
+Abu Sayed it's important to know that special relativity says that the speed of light *in a vacuum* is constant. if the light travels through any other medium it can be slower of course. to be fair this is actually a pretty common misconception around physics.
At the time, I was just using Cairo (C++ library). I tried a bunch of other solutions since then, but none have been as consistent. Working on a new one now!
Ok. I understood some things? But now i wonder about one thing. could you use the one lense where light can't escape (or a close aproximation) to extend the time wich would be needed to create a kugelblitz? Because as far as I understand it (and I don't) for a kugelblitz to form you need a whole bunsh of light in the same spot at one time. a black hole worth of light actually. And the "perfect" lense could trap light indefenetly, but scince you tell me that's impossible, could we just extend the time frame, and cheat the kugelblitz? Theoreticly of course.
I looked into this a while ago, but had no idea how to properly simulate it. The problem here is that the closer the light gets to the center, the slower it is moving. At some point, it "stops" almost entirely. Basically, this system is ill-suited for that purpose; however, I looked into some numerical relativity methods a while ago that could be useful?
I don’t know how difficult it would be, but it would be interesting if you could figure out a way to make an add on to render these impossible lenses in blender. While the 2D representation is cool, it doesn’t really explain what you would actually see if you had these lenses available to you.
Perhaps. If you manage to create a perfect lens like this and put it surrounded by lots of R136a1 stars, there's a small chance of making a Kugelblitz.
I wonder, could you create a mirrored lens? That is, a lens in which the light is trapped and then redirected back in the exact opposite of it's original vector?
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The first lense represents a black hole, a singularity at the center as gravity has an index of refraction, known as a shapiro delay.
Thanks!
Really wish I knew what I was watching.
Its fun tho. i think. LENSES! YEAH!
Yeah, true
You guys are watching a cool video! Thanks for being awesome!
YAY LENSES
Its basically looking through your glasses on steroids.
This kinda reminds me of 3Blue1Brown :) and as always very nice vid!
By the way, I was wondering what could happen if there were, say, two places where the lens had a peak in refractive index? More peaks ? Though tht would make n a function of r and θ as in polar coordinates, else I think that wouldn't be possible?
Another idea : absolute value of a tangent function? How about just the absolute value of r?
Probably not very interesting cases, but thereyago.
I just found out about 3blue1brown the other day, we are not too far apart.
As far as the lens is concerned, r can not go negative, so the abs(r) may not be too interesting. I don't remember if we tried the tangent or not.
I am fairly certain that if we saw two peaks, light would be attracted to both peaks and you would see the rays moving towards whichever is closest. I am not sure, though. Definitely something to try!
Oh, yeah, that would be just n=r then, that wouldn't be very fun.
I really wanna try and reproduce your simulator now, though! Great work!
It's all available on github (it's not the cleanest, but it uses c++ and cairo): github.com/leios/simuleios/tree/master/geometrical_optics
It's basically following the vector form of snell's law in a time-dependent manner by taking into account the changing velocity of light.
Won't the lens at 2:47 become invisible?? As The light rays passed straight through!
Yeah, that's basically just "glass"
"basically just glass" no, because the edges are not straight and parallel. You appear to have a constant IOR as the rays pass through the bulk, since they are straight lines. But the IOR at the point where the ray enters must be just right to match the angle of the ray's intersection with the edge, which varies continuously since the profile varies.
Even I thought that.
It would be like the vantablack of lenses in that it would be like 99.999% invisible but not fully invisible.
That's what he said. And the name "Invisible Lens" is pretty much the spoiler alert.
::facepalm::
The situation were the light enters the lens and cannot escape is rather like a Black Hole.
Yeah, it's awesome!
Even if we can't get a refractive index higher than 36, I'd still like to see what that lens looks like up to 36. Either have a core of 36 for all r where the intended index is higher than 36, or shrink it so only the center point is 36.
I suspect the math itself might be similar. After all infinite refractive index = lightspeed reduced to zero. Which in a sense is what happens to light falling inside a black hole, from the point of view of an outside observer.
I wonder if there's some deeper correlation between the R/r lens and real black holes. Do both phenomena follow the same equation?
No, they follow very different equations :) Black Holes capture stuff because of immense gravitational pull caused by their immense mass, and the lense captures light because it follows the fermat principle, which basically makes light bend towards greater refractive indexes
This is a great video. I’ve been a lens designer for 44 years and I developed a large scale gradient index glass known as GRADIUM in the early 90’s. I’ve played around with different gradient geometries but have never seen a video simulation like in this video.
What software were you using and how did you make it look like real time ray tracing while varying the parameters?
Really cool. Good job.
Please get back to me. I’d like to discuss gradients with you and tell you about some of the new 3D glass printing we are doing (including gradient index glass)
Thanks,
Paul
I actually developed the code myself. It was written in Cairo (C++ library). Each visual took a super long time, but if you want to replicate it, I would probably just do raytracing like normal and then after the light ray intersects with the object, switch to a timestepping scheme where you move the light forward by some dt every step and use the new refractive index at the new location to figure out how light bends.
I thought about doing a full 3D visualization, but honestly didn't want to model a 3D environment and showing the rays in this way is actually more clear to the viewers.
If you want a nice lens concept, try the Cloaking Lens: take the "Invisble lens" concept, but make it so the refractive index diverges before reaching the center (before radius r= 0, at r=k), that way you perhaps you'd be able to put an object in the middle with light going around it and leaving in the same direction?
I need to think about what the equation would look like for that one. My fear is that the rays entering the lens with a position of x < k (measured from the origin), will not be "invisible" and will instead hit the object.
What does the effect of an equation with a singularity outside the origin look like? a simple example would be (R-k)/(r-k). Indeed at least one ray must hit the singularity, even in the invisible lens case (the central ray). Actually looking at the inv. lens paper, what if you replace every instance of a/r (or R/r) in the n(r) formula for (R-k)/(r-k)?
just tried it, all the rays enter and move towards the assigned value for k, at which point, the refractive index is way too high and the rays cease to move. I suppose we could gloss over that by forcing the index to remain under a certain value, though.
Oh interesting! Looks like a cool problem :) I'm thinking the solution might be diverging the rays before hitting the singularity? (so maybe a ring of index
Gustavo Ramires honestly, attacking this problem analytically is probably difficult for anyone. I certainly did not attempt it!
bro you're insanely good
Thanks, you too!
So cool. Thanks for posting!
I'm glad you like it!
Oh man thanks you created this with c++
Yeah, it's been forever since I wrote it and the code is messy. I've been meaning to redo it in OpenGL, but I just haven't found the time.
+LeiosOS, in my school we are using turbo c++ will this code work on it? Pleeeeaaaase tell me which compiler you used!!!!
I just used g++, but I used Cairo for the visualization, so you will need to load that. As a side note, the reason I want to redo this is because Cairo is a vector-drawing library, which means that it draws an image at a time and outputs it to file before mving onto the next image. This is prohibitively slow and meant that in order to create videos, I would need to create a huge number of images and string them together at 60 fps.
LeiosOS thnx :)
LeiosOS well, aren’t you recording the video in real time , like simulating it using the code , why do you need to produce many different images , can’t the same thing be achieved with code , like , if we consider a point at the tip of the moving light Ray , which leaves its trace as it moves , we would just need move/trigger that point into a certain direction from the origin and it will just trace(color) the desired Ray path, is there any problem in this approach, maybe it won’t generalise ! Or will it?
I'd like to make some kind of real-time raytraced simulation to experience in VR. That's probably as close to 'experiencing' theoretical optics as we can get. It would be fun to add some lasers and other various visible light emitters, with some prisms and mirrors and everything else to setup a 'table' for experimenting on.
Oh yeah. That would be super cool!
Light doesnt literally move slower. It just takes longer to move through the material, due to more particles getting in the lights way, so it has to bounce more.
That's one way to look at it. But regardless, the net effect is the same. Right? Light "slows down" in a lens and we use the difference in velocity to measure the index of refraction
+LeiosOS Very true. I was merely pointing this out because this is something that gets misunderstood a lot.
Thanks!
The invisible lense is a nice way of "slowing down" light by making it go a longer path without interrupting it
Yeah, basically. In principle, there's a way to hide something inside the lens too... but I don't know much about that.
"The light can never escape..."
So what you're saying is, a black hole. Which means this lens does actually exist in nature. ;D
Yeah, maybe. I don't really know how this relates to a black hole.
This is so awesome. I'm a CS student at communtiy college and I'd love to see a video on how you made the code for this animation. Maybe even explaining some of the physics concepts like Snell's law and showing how you implemented it into code. I'm a huge fan of your work please keep these videos up I assure you you are inspiring many young thinkers!
Ah yeah, this was all live on twitch. I might do a "making of" video soon, though. Thanks for the suggestion!
this was awesome!! I'm currently learning about waves and optics in my college physics class
Yeah, it's super cool stuff!
Saw you on reddit. Hope your channel explodes! I subscribed instantly!
Thanks, I'm glad you enjoyed it! =)
I have c4. I can make that happen.
This video is in my recomended, I clicked on it, didn't regret clicking on it, this video is great.
Woo! I'm glad you liked it!
That blackboard is pretty cool.
Yeah, it's black. =)
Not the weirdest thing I watch in my recommendation but it’s right up there
I am glad you watched it anyway!
The beautiful part about the last one is that the very small entering index would unsure a very dimm reflection. However, I think it's should be noted that shape has to be spherical for that specific gradient to work.
It would be really interesting to find the invisibility index grading for a non trivial shape in that program.
Yeah, they did a great job figuring out that lens in the paper! What do you mean "invisibility index"?
LeiosOS oh, I meant that I would like to see what the strength map of the refractive index for a non-spherical arbitrary shape would be. For example a concave polygon, would it even be possible to be made invisible?
I bet Renderman or Vray could show what it would actually look like. I use Renderman, if the refractive index is constant throughout the sphere I could probably recreate it if I knew what to input into the material settings.
wait, recreate what what would actually look like? Do you mean for full 3d visualizations? For each of the unusual lenses, the refractive index varied on the inside of the lens, so it'll be hard to implement, but certainly not impossible!
LeiosOS you could make a volumetric shader
Just a minor correct, the light doesnt actually slow down when it hits the medium, It just travels a further distance through it giving the resultant effect of slower without actually slowing
Wait, is that true? I always thought the refractive index was defined by the change in speed as light enters different media: math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html (first couple of paragraphs)
Yeah, the light does physically take longer to go through the material, but its not slowing down taking a longer path through the material.
Really cool video man! Good work
I'm glad you like it! =)
I watched this in 2018 and was looking for Information of this kind for about 25 years. very interesting, maybe some of these lenses will be made in the future.
That's definitely an area of active research!
The lens at 1:36 (96 s) though seems like it would approximate a black hole in some ways, because a black hole bends all the light that falls on it into itself and absorbs it completely - and this effect is, after all, called "gravitational lensing". Granted, the _speed_ of the light doesn't change, but the point is that it can affect the _geometry_ of the rays in a similar fashion, and thus there _is_ a natural analogue, if perhaps not exact, for this case. If you were looking at this lens, it would look like a black circle, which is the same way the horizon of a black hole would appear to you.
For the other lenses, while they may not be real-life realizable, it'd be great to see them realized virtually in a computer raytracing simulation, so we could see what it'd actually look like to look through them, _were_ they to be able to exist. I wonder if POV-Ray or similar computer graphics software could be used to achieve this. Really would be interested in seeing what it'd look like to look through the lens at 2:24 (144 s).
We had to develop a specific time-dependent raytracing method for these lenses so we could more accurately trace the light as it moved through the lens. I feel there is definitely a way to work with these in other software, but I am not sure...
For a lens, i'd love to see solutions to differential equations for the function. Maybe like a solution to the logistic equation or something similar. I wouldn't be surprised if you could draw some sort of real world conclusions from it too with a bit more work.
What do you mean "solutions to differential equations for the function"? Could you give an example?
I'm glad I found this
That's very interesting! if I'm understanding correctly at least related to an idea I had you could use it to focus a magnetic field to a fine point using something like a lense. basically creating a focused magnetic field using a laser instead of magnets. you made it easier to visualize thanks!
I'm glad this helped out! I don't know much about magnetic lenses, though.
I know it doesn't make a lot of sense it just helped me visualize a possible way to utilizes a metamaterial.
I would like to see a video about negative index of refraction. I hear some meta materials and mirrors can achieve this.
Yeah. I avoided that for this video because it's super hard to understand
For better visualisation, you might want to colour the rays of light in a gradient from top to bottom (of input). That way, instead of just seeing that rays end up somewhere, you see at a glance /which/ rays end up where. This would be especially useful when sweeping through a range of values. It would give you more of an idea of the image on the other side.
Obviously it's now a while since this video was made, and I haven't checked to see if this project is still active, but I thought I'd share the idea!
Yeah, I could see that being useful. Sending in a rainbow of colors would be nice.
I would love to see someone doing the same thing but with Gravity instead
Like gravity waves? That could be possible with FDTD simulations.
I had more in mind changing the formulas of the force of Gravity
For instance, how would an orbit look like if the force of Gravity was depended not on the Distance squared, but the Log of both distance time pi
or perhaps other formula I can't think about due to my limited knowledges of maths
Basically, exploring similar concept as you did with the lenses
So we could create a light bomb with a lens? Sounds dangerous
Really interesting video!
Yeah, it could be dangerous. Probably why the lens cannot actually be made.
Invisible lens? More like glass. Nice video.
lol but you're probably right, friend
It's like glass, but with a delay.
Amazing video, thank you for the good work
Thank you for watching!
I have a question. From what I understand, the slower speed of light in a dense medium is not due to the individual photons slowing down. Each photon still moves at C, no matter what. Light appears to slow because the photons take a more meandering path when there's a bunch of mass in the way. So my question is this: why do all the photons end up in the same trajectory if they're each following different meandering paths?
For the approximation we are taking here, it's not obvious that the light is taking a "meandering path." We kinda just ignored it for this. It's a lot easier to think of this when you think of light as a wave, not a particle... but even that is unclear until you start talking about individual atoms and such. I think this gave a decent description of the phenomenon: physics.stackexchange.com/questions/105573/why-does-the-light-travel-slower-in-denser-medium
I want to see some ray tracing simulations with these lenses.
WOW! As a stage lighting technician, this is amazing to me.
Wow! You sound like you have an awesome job! =)
The first impossible lens could be the exact reason on why light can’t escape the black hole since if times the gravitational pull by the index it could lead to mass and/ or density.
Ah, maybe. I don't know exactly how it relates to a black hole, but gravitational lensing is a thing, so maybe this is also a thing?
LeiosOS i figured out a short equation it’s
n(r) = R/r x g. But that’s just on the top of my head
When people talk about doing the impossible, I wasn't exactly thinking of impossible lenses.
That last lens could be the key to a invisibility cloak
Oh yeah, people are working on that now! Super cool research!
Having Toby Maguire explain physics to me is one of the best experiences I could ask for
Yeah. I am often told I look like him.
i'm pretty sure light only bends going from one medium to the next but in your case light is continuously bending as it travels through the lens. Also if you're going to do theoretical lenses, what about a negative index of refraction ;)
Light is continually bending because we chose a continuously varying function inside the lens. Also, I didn't know how to interpret negative indices... but that might be a good thing to try!
Ah you sound like a male Vi Hart tbh! I like your voice. Very soothing/pleasant to listen to. The animations are neat, as well.
I am glad you liked the video! I wish I could work with Vi hart on a video. Her stuff is great!
How do you create all those AWESOME stimulations? :O
Here, we did raytracing. We just followed the light by solving snell's law for a constantly changing index of refraction. Super fun to code up!
I see how you could have done a simple check when it entered a lense to change the angle. How did you change the angle gradually or curve when it was inside? You said it is vector graphics, so you calculated it every pixel or what?
I thought it might be interesting to use refractive indexes as a complex function visualisation. `C (x,y) -> C (z,Index)`. What do you think this might look like for some hard to visualise complex functions?
I have an invisible lens in my house, actually! Most people that come over don't call it that though, they call it by some odd, alien term known as "glass"
Yeah, it's class, but spherical. Imagine a sphere of glass that you see right through like ti doesn't exist (except for a small delay of light)
LeiosOS for the most part you can do that with a bottle of windex lmao
Nah, if you put windex on it, it becomes the first lens in the video
Ooo... I tried to think about it way back in maybe 2012 or 2013 so I was very young and not sure how much what I'm about to say is right but I was very confident about what I did then... What I found out that if you define these functions of refractive index as a function of position and if you precisely know the momentum of photon you're about to shine then Heisenberg's Uncertainty principle should kick in and ruin everything you're trying to do because by knowing the refractive index and initial momentum, you can figure out the final momentum so if you're certain about initial momentum then you can be certain about the final momentum or in this case the momentum at a perticular position but now according to uncertainty principle you cannot be certain about momentum and position simultaneously and defining refractive index as a function of position exactly does that...
So all these lenses are impossible lenses which have their refractive index defined as a function of position...
WTF you serious?
Light is not moving slower at all, light is always traveling at lightspeed! It just takes a longer way which needs more time to travel.
Daniel Reinhardt light travels at different speeds depending on the medium lol
Do not know why it was recommended to me, but stuff is good!
I am glad you liked it!
Is a lens possible, in which there would be a preferred direction/helicity of light rays/that 'twists' light? I mean not the polarization, but in the handedness in which the rays swirl around the center. That way, we could not only model a Schwarzschild blackholes causal structure bellow its horizon, but also the frame dragging/lensing of a Kerr black hole.
have you considered an index of refraction that changes with frequency?
The highest index of refraction we can find in nature is a black hole :p
You are not wrong... =)
Also not right...=) Spacetime is warped, but the light is still going straight, so no refraction.
how do you take into the account of high index of material + wrap spacetime?
you cannot just add them.
Roel Lemaire Actually we can assimilate the bending of spacetime with a "void refraction index", and the effect is mathematically accurate ! Such an index would depend on the angle of incidence Theta and the distance from the black hole R : n ~ 1 + (GM/Rc)*(1 + cos(Theta)^2)
learn something new every day!
thanks!
Is it for Schwarzschild black hole only?
does it have a boundary condition and PDE it satisfies?
ok youtube. the algorithm landed me here at 2am, you win.
Well, I am glad you are here!
Very cool! Esoteric af!
Just a bunch of math. I like math.
add those to cycles and render a photo-realistic preview of them
We could probably do that. We had to do some tricks to get the ray-tracing to work here, but we could do that with a much larger number of rays to get a similar effect.
Invisible Lens, also known as a pane of glass.
U Wot M8 light that goes trough glass bends while the light that enters the ijvisible lens doesn't
A sphere of glass that looks like a plane of glass with a slight delay
Unless the light is perpendicular to the pane of glass, the light will be shifted to the side by an amount proportional to the thickness of the glass.
The "invisible lens" doesn't cause the light be shifted.
Thank you very much, this is a very nice visualization! What did you use to make it?
We wrote our own visualization library with Cairo and C++
This guy is really likeable. This is gunna take him far
I like you. You are cool!
Like the lens that has an infinite index of refraction at the origin, how about a lens that makes incident light always travel tangent to the radius such that it perpetually orbits the origin?
I'll have to keep an eye on this ;)
The best Doctor
Thanks. Not a doctor yet, still working on my PhD.
Great video! May I ask the names of the tracks you used in this video? I searched through Josh Woodward's site but I couldn't find them.
Honestly, I am not sure. I looked for which ones exactly, but cannot find them. They were sped up for this video. I am sorry!
Be neat to put some of these through 3d software...though hopefully not blow the cpu up with div/0 stuff. The second one, isn't that a black hole due to extreme gravity capturing the light? Really neat vid!
To be fair, at some point we had to approximate the center of the lens anyway because of the divide by 0 problems. The lenses still seemed to work.
You can also get an invisible lens by setting the refractive index of the lens by 1.
1:49
Sounds to me like a black hole can literally make this lens a reality.
Yeah, I am not sure the black hole's index of refraction.
LeiosOS
Well, I'm pretty sure they're not identical, to be fair. Just similar enough to make that comment.
I have no idea what's going on, but that's awesome
Haha, you're awesome!
I'd be interested in simulating these lenses with path tracing, so we could actually observe what these lenses would look like in real life!
Yeah. A lot of people have wanted to do this. I think part of the problem here was that we used a special method to do this simulation that was "time-dependent" so normal raytracing methods would break down at some point.
Refractive index = e^r
Hmm. I think I can pull out my old code and see what that looks like. I fee like we tried it, but I don't remember it.
The light source of these experiments were all parallel, as if the lighsource was infinitely far away. How would the light rays travel through the "invisible lens" if the point of origin was, say, 1 diameter of the circle away?
Ultimately, this would cause a lot of scattering, but because it's a spherical lens, there wouldn't be too much that changes with the actual raytracing here.
1:40 If you shine at it long enough, you'll form a kugelblitz!
Ooh. Ball lightening was something I looked up before, but couldn't figure out how to simulate.
Not a ball lightning, a black hole made of light!
Now I'm wondering what happens if you do the double slit experiment behind the invisible lens. Do you get a different result than without the lens if both the slits are behind the lens/only one slit is behind the lens?
The results should be similar. The only thing the invisible lens does in practice is add a delay to the light.
I don't find the formula for the invisible lense anywhere and the link in the description requires to pay
Thanks for bringing this to my attention! I've added a link that is not behind a paywall in the description. Here is is again: iopscience.iop.org/article/10.1088/1367-2630/13/8/083007
Wow, great video!
Thanx! Great! Please, make more about optic!
We might pick up something like this again soon, except for the wave nature of light. In fact, there is still a good bit left to do with ray optics. Let me know if you have any ideas!
Someone should make a simulation to show what these lenses would look like.
Electroflame 618 very very trippy...
You can make it if you want to!
I guess infinite refractive index cam be seen in nature. It could be at the singularity point in the black hole where it has 0 volume and infinite density. So maybe it can be said that the singularity point is the brightest? I dunno. Just guessing
If you allow for anisotropy, you can do the cloaking device lens!
Oh, I don't know about this one. Could you provide a formula?
Sure thing! The cloak is two concentric cylinders, inner radius a, outer radius b
Anything within the inner radius is cloaked, so index doesn't matter.
The lens part, between a and b, has anisotropic permittivity and permeability, defined in cylindrical coordinate directions, namely:
ε_r = μ_r = (r - a)/r
ε_θ = μ_θ = r/(r-a)
ε_z = μ_z = (b/(b-a))**2 * (r-a)/r
(science.sciencemag.org/content/314/5801/977/tab-pdf paywalled)
So why is it impossible to create the "Black Hole" lens where the light bends infinitely inward?
Because it's impossible to create that refractive index function in a lab.
So would the invisible lens be like a mirror?
More like glass with a slight delay.
Lenses like this sort of exist in nature in the form of black holes and gravitational lensing.
Some of them might.
Well,but how does the speed of light inside any lense reduce without breaking s. relativity theory?why do we still use refractive index=c/v when relativity says the for an arbitrary observer speed of a photon remains constant ?
So, this is a bit of a weird answer, but light seems to slow because it is constantly absorbed and then re-emitted, which makes it appear slower.
I would also like to add in wave-particle duality. While the wave will slow down, the particle part is still traveling at C. It's just not taking the fastest route possible. So, it is both slowing down and staying at the same speed. It just depends on if you want to talk about light as a particle or a wave. (By the way, I am just a high school student who watches a lot of educational TH-cam, so if you really care about knowing the answer, google will probably be a better friend than I).
Abu Sayed Or even better, look it up on Quora. Actual physicists are known to answer questions there from time to time.
+Abu Sayed it's important to know that special relativity says that the speed of light *in a vacuum* is constant. if the light travels through any other medium it can be slower of course. to be fair this is actually a pretty common misconception around physics.
MinutePhysics has a really good video about this: th-cam.com/video/FAivtXJOsiI/w-d-xo.html
Can you make a lens that is hollow, and makes inside invisible when viewed from all directions?
I think there is current research in the area, but I am not sure.
The invisible lens thing, wouldn't something happen to the light in some way? Maybe make it slower or something?
Yeah, there's a slight delay
How about one where the refractive index is the inverse of the number of light rays within the lens?
Ah, this would be a bit off with an index of < 1, but should be doable.
What is the program that maps equations to these wonderful animation
At the time, I was just using Cairo (C++ library). I tried a bunch of other solutions since then, but none have been as consistent. Working on a new one now!
That's a nice little code you have there...
... Would be sad if reality came along and broke it, wouldn't it!?
Look, the code is almost always broken. That's the nature of programming. Compilation errors out the wazoo.
Ok. I understood some things? But now i wonder about one thing. could you use the one lense where light can't escape (or a close aproximation) to extend the time wich would be needed to create a kugelblitz?
Because as far as I understand it (and I don't) for a kugelblitz to form you need a whole bunsh of light in the same spot at one time. a black hole worth of light actually. And the "perfect" lense could trap light indefenetly, but scince you tell me that's impossible, could we just extend the time frame, and cheat the kugelblitz?
Theoreticly of course.
I looked into this a while ago, but had no idea how to properly simulate it. The problem here is that the closer the light gets to the center, the slower it is moving. At some point, it "stops" almost entirely.
Basically, this system is ill-suited for that purpose; however, I looked into some numerical relativity methods a while ago that could be useful?
Isn't the first "impossible" lens just a black hole?
Yeah, I have been told it's something like that.
i was watching mustang crash videos. how tf did i up here.
TH-cam man. No one knows how it works!
I don’t know how difficult it would be, but it would be interesting if you could figure out a way to make an add on to render these impossible lenses in blender. While the 2D representation is cool, it doesn’t really explain what you would actually see if you had these lenses available to you.
I have been asked to do this, but I don't know how to do it, myself. I wish I could, though!
LeiosOS, I don’t know anyone, but maybe you could find someone who can do it. There are a lot of people who make blender add ons.
the fcuk did i watch? my brain be like i watched an invisible video
You watched a video I made on some cool lenses. Thanks for watching!
01:35 Could we use that to make a swarzshild kugelblitz ?
I don't know, to be honest... But I think not.
Perhaps. If you manage to create a perfect lens like this and put it surrounded by lots of R136a1 stars, there's a small chance of making a Kugelblitz.
It would probably turn into plasma (another thing we should name) before anything even started to think on happening
I wonder, could you create a mirrored lens? That is, a lens in which the light is trapped and then redirected back in the exact opposite of it's original vector?
This would take some testing, but we could try!
I LOVE watching this kind of video
and pretend I'm smart enough to understand it.
You are smart enough to understand it, no question about it!
So light slows down then speeds back up again
Yup. Lenses are cool!
I have a full invisible Holographical Optical Element System incl, ultrasound hearing, subvocalisation silent speech, invisible luneburg superlens for Virtual Reality with over 40 tools for augmented reality.
Great video man thanks
I'm glad you liked it!
If we make a lense that no light will pass through center we could hide stuff in it?
I think that's an area of current research.
Do we have a material that gives similar refraction angle for different wavelength? If not cloaking lens wouldn't be possible.
A black hole is, quite literally an invisible lens
Well, I feel it's the opposite of an invisible lens.
LeiosOS a extremely visible lens?