Telescope lenses and the lenses in our eyes are not strictly necessary for detecting individual photons from distant galaxies, but they do help to focus the light and increase the number of photons that can be detected. Photons are elementary particles that carry electromagnetic force and are the basic unit of light. They have no mass or size, but they do have a wavelength that determines their energy and color.

In a two-slit experiment, individual photons can pass through both slits simultaneously and interfere with each other to produce an interference pattern. This behavior is due to the wave-particle duality of photons, which means that they exhibit both wave-like and particle-like properties.

In the context of observing distant galaxies, telescope lenses help to collect more light from a specific source and focus it onto a detector. This increases the number of photons that can be detected and improves the sensitivity of the observation. Similarly, the lenses in our eyes help to focus light onto the retina, allowing us to see distant objects more clearly.

The "diameter" of an electromagnetic wave is half its wave length.

Montie, E., Cosman, E., 't Hooft, G. et al. “Observation of the optical analogue of quantized conductance of a point contact”.

Nature 350, 594–595 (1991) https://doi.org/10.1038/350594a0

With kind regards, Sydney

Let's say you have a telescope with a 10 cm circular aperture; and also a disk-shaped photon detector, with the same diameter of 10 cm (e.g. a 10 cm square CCD with a circular cutout aperture mask laid on top). There are no optics in front of the circular sensor.

Point them in the same direction of the night sky. Over a given time period, they will detect/collect the same amount of light flux from any given star or galaxy (plus sky background). So to answer your initial question, "are lenses necessary for detecting individual photons from distant galaxies", the un-nuanced answer is: NO, they're not needed.

Early x-ray astronomy detectors worked on this principle. It is extremely difficult to focus an x-ray photon, so they didn't try...they just caught them on a bare, large-area flat detector. Multiplexing tricks (coded aperture masks, modulation collimator) gave coarse directional information for the x-ray sources, many of which were galaxies.

The more nuanced answer is that focusing optics (lenses, telescopes) give us directional concentration of signal, which makes it far easier to discriminate a particular galaxy's photons from all the others landing on the same collecting aperture.

In the little experiment I described above, all the celestial sources splat photons uniformly across the 10 cm aperture/pupil plane. But only the telescope can redistribute those photons into tight bunches in a focal plane, correlated with exactly which object in the sky emitted them.

So there's detecting in the sense of

• "did my detector register a response to these 100,000 incoming galaxy photons? Yes, but they're buried in 100 billion other photons"

...and then there's detecting in the sense of

• "can I make these 100,000 incoming galaxy photons separate from the others and form an image of the galaxy, at good signal-to-noise ratio?"

Lyudmil Antonov, I can't quite grasp how anything that can be said to exist can have no size (though I *can* imagine that that size may be too small for us to measure). I suppose people have made systematic studies of slit spacing in the two-slit experiments for various wavelengths of light, to see the limits of slit separation. Sydney Ernest Grimm offered a paper that suggests a photon width is half its wavelength (though I was in over my head just reading the abstract--need to brush up on plane waves, etc.). I'd like to understand that work.

Ray Butler I really liked your answer, in that it addressed my question well and was understandable to this non-expert. I had been wondering if individual photons consisted of something like an actual "wave packet" that goes in and out of "focus" onto a point in space, and wondered if they can react with a detector only when their energy is concentrated at a point. I was thinking naively that maybe a lens would force a focusing, but now that I think about it, that seems silly, as it might "defocus" as many as it "focused." Thinking about your answer suggests to me that astronomers probably have a good idea how many photons are coming from a specific galaxy per unit time, using lenses, and been able to compare that number to the merely collimated (i.e., non-lensed) number that they could isolate (somehow) from that same galaxy. I assume those numbers always match up. But even so, I wonder if we're measuring all the photons in each case (not counting ones our detector is unable to see for technical reasons, like dead time). Could "out of focus" "wave packet" photons be escaping our detection?

I suspect that you need to slightly alter your question, as most telescopes don't use lenses anymore. Instead, they use mirrors. So perhaps the question should be phrased to specify the nature of the observation, rather than the structure of the device.

The size of a photon is not a well-defined concept, because photons are quantum objects that do not have a fixed shape or structure. Depending on how you measure them, they can appear as point-like particles or as waves with a certain wavelength. However, some possible ways to estimate the size of a photon are:

- The **Planck length**, which is the smallest possible length in physics, about **10^-35 m**. This is the size of a photon when it is localized as a point-like particle¹.

- The **wavelength** of the photon, which is the distance between two consecutive peaks of its wave. This can vary from very short (gamma rays) to very long (radio waves). The wavelength of a photon is related to its energy and frequency by the formula $$E = h f = h c / \lambda$$ where $$h$$ is the Planck constant, $$c$$ is the speed of light, and $$\lambda$$ is the wavelength. For example, a visible light photon has a wavelength of about **400-700 nm**².

- The **cross section** of the photon, which is the area that it occupies when it interacts with other particles or fields. This can depend on the polarization and angular momentum of the photon, as well as the type and energy of the interaction. For example, the cross section of a photon scattering off an electron can be calculated using the Compton formula $$\sigma = \frac{\pi r_e^2}{2} \left( \frac{1 + \epsilon}{\epsilon^2} \left( \frac{2(1 + \epsilon)}{1 + 2 \epsilon} - \frac{1}{\epsilon} \ln (1 + 2 \epsilon) \right) + \frac{1}{2 \epsilon} \ln (1 + 2 \epsilon) - \frac{1 + 3 \epsilon}{(1 + 2 \epsilon)^2} \right)$$ where $$r_e$$ is the classical electron radius, $$\epsilon = E / m_e c^2$$ is the ratio of the photon energy to the electron rest mass energy, and $$\sigma$$ is the cross section³. For low-energy photons, this gives a cross section of about **10^-28 m^2**⁴.

(1) What is the cross section size of a photon? - ResearchGate. https://www.researchgate.net/post/What-is-the-cross-section-size-of-a-photon.

(2) Photon - Wikipedia. https://en.wikipedia.org/wiki/Photon.

(3) What are the dimensions, width and length, of a photon?. https://physics.stackexchange.com/questions/161055/what-are-the-dimensions-width-and-length-of-a-photon.

(4) What is the size of a photon? | Notes and Queries | guardian.co.uk. https://www.theguardian.com/notesandqueries/query/0,5753,-4723,00.html.

(5) quantum mechanics - What is Size of Photon? - Physics Stack Exchange. https://physics.stackexchange.com/questions/206772/what-is-size-of-photon.

(6) Is the size of a photon dependent on its wavelength?. https://physics.stackexchange.com/questions/103904/is-the-size-of-a-photon-dependent-on-its-wavelength.

There is another reason why Sydney Ernest Grimm is right. It is very simple. Any photon, in order to reach the receiving element or screen, needs to travel a path equal to an integer number of its wavelengths. The next allowed point of its incidence can only be a point, the path to which differs from the previous one by one wavelength. The distance between these points can be roughly considered to be a half of the photon wavelength.

This will be just a required photon "width".

Sincerely, Dulin Mikhail.

Mikhail N Dulin --- I'm not sure I understand your point about the photon needing to travel an integer number of wavelengths to be detected. I assume you mean that if it's detectable at one place along its sine wave disturbance of the EM field, it'll then be detectable only when it reaches that place again. I'm thinking there must be something about that rate of EM field change that jibes with the rate of atomic electron orbiting of the nucleus of the atom it happens to interact with in the detection process.

In any case, I'm not sure how you went from a full wavelength to a half wavelength for the "size" of the photon. (I'm actually thinking more of what Lyudmil Antonov mentioned---the cross-section of the photon. But, there's a lot to digest in his very thorough and detailed answer---for which I'm grateful!)

Courtney Seligman ---you're certainly correct, in that I could've added the words "or mirrors" after the words "telescope lenses" in my question, to be perfectly clear that it's only the light gathering/focusing power of the lenses that is relevant.

Dear Harold Kyriazi.

The question of the transverse size of a photon is very important, and I welcome your desire to understand it. Moreover, photon as a quantum object may not have a transverse size at all. Instead, we can only know about the diffraction properties of an ensemble of photons by observing the pattern, for example, behind a small hole or slit. Two neighboring photons in a wave incident on the edge of the slit can be considered separated by their "width" if only they fall into the neighboring maxima of the diffraction pattern behind the slit.

Your example with the photon falling on an atom, in my opinion, will not give anything, since the wavelength of light, say, in the visible range, will be much larger than the "size" of the atom. Only particle that ceases to be a Rayleigh's one with a huge number of atoms in it can say something about the wavelength of the photon and its transverse "size" in a certain sense. When we notice the quadrupole scattering of light by this particle.

But your question at the beginning of the discussion was very good! Sincerely, Dulin Mikhail.

With apologies to all, since Courtney Seligman's comment alerted me to the fact that the "questions" posed and posted here will remain as teaching tools for others (and not just ephemeral musings), I decided to go back and alter the initial question a bit, to more accurately reflect my thoughts.