How a Lens Creates an Image, low NA vs high NA, Huygens OpticsVideo

[RobertOToole]

Found this video just this morning. Very interesting NA and diffraction examples with excellent animation examples using waves instead of rays.

Definitely worth 20 min for anyone with an interest in optics.

Video: How a Lens Creates an Image

Link: https://www.youtube.com/watch?v=SS2AbZVdk2A

Huygens Optics

Contents:
0:00 Introducing "rays"
2:14 Light is a wave
4:00 Nils reached one thousand!
4:43 Effect of Numerical Aperture
6:46 About "Critical Dimension"
7:40 Effect of NA illustrated using a microscope
10:44 Diffraction in the Double Slit Experiment
12:30 Diffraction in the Circular Slits (Fresnel Zone Plates)
14:40 Effect of central obstruction on focus
15:05 Using diffraction to create an Image
18:59 Comparison to the Fourier Series Approximation
19:44 Image Creation and JPEG compression
20:59 Effect of wavelength on definition
21:35 Extroduction

[jmc]

Just watched this and thought it was excellent (as are all his videos). Well worth a watch.

[chris_ma]

thanks for posting the video, I very much enjoyed the visualisations.

I find it a bit funny though, that he says that physic books use rays to simplify things, while in reality light consists of waves.
now while this model works very well for calculating optics, by today pretty much the whole physics world agrees, that light consists of particles, and the wave like effects are due to the randomness of quantum physics.
In other words, the wave model is useful for calculating things, but what he explains is actually not how nature works.

some of the best introductions to these topics for me were two lecture series by Richard Feynman in auckland and at esalen institute.
he even explains the effect of lenses and the fresnel disk somewhere on they way:
https://www.youtube.com/watch?v=xdZMXWmlp9g
https://www.youtube.com/watch?v=xdZMXWmlp9g

and more entertaining then scientific, but rather philosophical too is this one:
https://www.youtube.com/watch?v=P1ww1IXRfTA&t=1568s

[RobertOToole]

thanks for posting the video, I very much enjoyed the visualisations.

I find it a bit funny though, that he says that physic books use rays to simplify things, while in reality light consists of waves.
now while this model works very well for calculating optics, by today pretty much the whole physics world agrees, that light consists of particles, and the wave like effects are due to the randomness of quantum physics.
In other words, the wave model is useful for calculating things, but what he explains is actually not how nature works.
.........

Makes sense since afterall HuygensOptics is named after Christiaan Huygens (Dutchman came up with and published a paper the wave theory in the 1600s).

I'm not picking sides but I thought light was both?

Best

Robert

[chris_ma]

I'm not picking sides but I thought light was both?

that's a common way used to describe the fact that there is some really odd behaviour, which seem to contradict our conventional view of the world.
but quantum mechanics is extremely successful to describe this behaviour, to a point that there's practically no effect that can't be explained by it.

by todays understanding, light clearly consists of particles (well, at least in the same way that an electron is a particle). It's just that until we measure it, the probability of its location is described by a wave function.

simply put, the wave theory can describe certain optical effects very accurately, but completely fails in some other situations.
quantum theory describes all behaviours extremely accurately, including the wave like behaviour of small particles.

[rjlittlefield]

the wave like effects are due to the randomness of quantum physics

I disagree with that characterization.

My way of thinking is that the wavelike effects are due to interference of each particle's wavefunction with itself, following the rules of Feynman's path integrals.

There's nothing random about that part of the process. You just form a properly weighted vector sum of wavefunctions along all possible paths between where the photon starts and where it might end up. This part of the process is completely deterministic, and what it gives you is the probability of observing the photon at each particular destination, when you finally observe it anywhere. A graph of those probabilities looks just like the intensity graph that you would get from considering light as a wave in the first place.

The randomness kicks in only when you finally observe the photon. You might see it anywhere, but you're more likely to see it at the locations where the wave model of light says that the light would be bright.

Bottom line is that it works great to model light as a wave. The surprising part -- astonishing really -- is that whatever results you get with the wave model continue to hold even when you send individual photons through the system.

I often describe this as "each photon interferes with itself". This sounds weird, since interference is not a behavior that we normally associate with particles. But I think it's a very good summary of how things work out in the end, courtesy the particle's wavefunction.

For reading more about this stuff, I strongly recommend Feynman's book, "QED: The Strange Theory of Light and Matter". I found it to be remarkably readable, in large part because the exposition uses physical analogies rather than mathematics.

I can also strongly recommend https://arstechnica.com/science/2021/01 ... mechanics/ . It is a series that begins with the title "A “no math” (but seven-part) guide to modern quantum mechanics". In addition to the main text, I found it helpful to read and consider various readers' comments. The author of the series is very fond of framing all behaviors as quantum mechanics even when classic explanations work fine. His discussion of optical gyroscopes would make a good example, but getting into that would be too far afield for this thread.

--Rik

[chris_ma]

it's likely that I didn't use all the terms accurately, as my knowledge of quantum mechanics comes more as a hobby rather than in-depth studies...

Bottom line is that it works great to model light as a wave. The surprising part -- astonishing really -- is that whatever results you get with the wave model continue to hold even when you send individual photons through the system.

sure, it's a very good model for practical purposes and much simpler than having to calculate all the Feynman integrals. It just struck me as funny when he mentioned that the light-ray path is a simplification while in reality light should be explained by a wave model - which is a simplification in itself, that breaks down for certain experiments.

one of the most important points in Feynman's lectures for me was, that Physics doesn't explain "why" something happens. It just offers a model that gives predictions that match what we observe happening in nature (he has a nice analogy about the Mayas predictions in astronomy).

so the wave model works very well for predicting what happens with light in optical paths, but it's not really a complete model, and it's pretty clear that it's not what really happens under the hood.

quantum mechanics is an extremely accurate model, which can be used to predict nearly every phenomena apart from gravity. but even though it works fantastically well, it doesn't offer any explanation why the world works the way it does.

[Marcepstein]

by todays understanding, light clearly consists of particles (well, at least in the same way that an electron is a particle). It's just that until we measure it, the probability of its location is described by a wave function.

If light (photon) is a particle, then what is a particle?

[chris_ma]

by todays understanding, light clearly consists of particles (well, at least in the same way that an electron is a particle). It's just that until we measure it, the probability of its location is described by a wave function.

If light (photon) is a particle, then what is a particle?

that's a very good question, which I have no good answer to

I guess one definition could be that it's got a certain size and location once measured, but the really really strange thing is that it appears that pretty much everything is in a state of flux until measurement.

we know an electron has a mass and call it a particle, even though it too can only be described in probabilities until we measure it (now what exactly counts as a measurement is another rather difficult question).

the problem with quantum mechanics is that it completely contradicts the way we perceive nature as human beings, which makes it hard to accept, since it seems crazy.

I like how Feynman puts it jokingly: "This is how nature in our world behaves. Don't like it? Tough luck, go somewhere else!" (loose quote from memory)

[Marcepstein]

by todays understanding, light clearly consists of particles (well, at least in the same way that an electron is a particle). It's just that until we measure it, the probability of its location is described by a wave function.

If light (photon) is a particle, then what is a particle?

I like how Feynman puts it jokingly: "This is how nature in our world behaves. Don't like it? Tough luck, go somewhere else!" (loose quote from memory)

BTW, one of the best Richard Feynman books Ive read: Surely You're Joking, Mr. Feynman!, by Ralph Leighton and Richard Feynman