The Rayleigh limit

17:14of the day is a wave, right? And so so if I have two, let's say I have two light bulbs that are right next to each other, if they're right in front of my face, of course I can discern them, right? Because my eye acts like a tiny little telescope and it creates an image in the back of my retina. And if the light bulb A goes to a certain part of my retina and light bulb B goes to another part of my retina then I can discern that there are two light bulbs because these rods and cones are saying hey I'm seeing a light bulb over here. These rods and cones are seeing saying hey I I see a light bulb over here right and so the two the two light bulbs are not overlapping in my detector and

17:55therefore I can discern the two. Now there there comes something called the rally limit which is if I take those two light bulbs those two points of light let's say tiny little LEDs and I take them really really far away all of a sudden they merge into one LED why >> right >> why because because the LEDs the the image in my retina is now getting overlapped because of the wave nature of light my pupil is only this big and so the the the the wave nature of light is going to like defract in my pupil and that's going to cause a blur uring effect that is just purely due to the wave nature of light. It's there's nothing I can do about it. There's no like oh put it in a vacuum, put it in

18:36cold, nothing because of the distance and the fundamental uh uh the fundamentals of how light travels over distance. As you increase that distance away from our own detectors, which are our eyes, >> the farther the distance away, the more overlap will happen between two independent light sources. >> Exactly. >> Uh they could be very far away. >> Yeah. >> But the farther you go away, they become it becomes hard to discern that there's a gap between these two. >> Yes. And so how do how do we how do we do anything, right? Um well, we make the the the detector bigger, right? We make our telescope bigger. The eye is a terrible detector. It's only about like

19:17less than a centimeter in diameter. Um that's why we have large telescopes. The larger the telescope, the the smaller the angular resolution that you can have, right? Um or I should say the greater the angular resolution, the smaller the angular distance you can discern between two independent points. >> Which is why we continue to Why do we need to make bigger and bigger telescopes, right? Because the bigger we make them, this is why, for example, between Hubble and JWST, we have fuzzy versus less fuzzy. There's different wavelengths in there and there's details. Yes. But fundamentally speaking, >> we have giant Mellin that's coming out versus regular Mellin. Why do you need

20:00to make a bigger Mellin? Because we like 4K TV. Yes. >> We don't like 720p. No, >> we don't like fuzzy CRT TV. We want to see every blade of grass. Exactly. >> We want to see every tear drop that comes from the face. And you can get that from making your detector larger in order to resolve light to more of a level a better level of granularity. >> Exactly. And if we're not going to settle for 720p on our TVs, we shouldn't settle for it [laughter] >> in astronomy. You know, you know what I'm saying? >> Yes. >> Come on, guys. 100%. >> Um, so, so the rally limit, that's that's that's the fundamental trade-off that we have. Okay. Now there's two ways to make your resolution better. Okay. Um

20:42the the the the smallest angular resolution that the smallest angular distance that you can discern is given by the rally limit. It's effectively the wavelength of the light divided by the diameter of your aperture. The diameter of your telescope. This is something that we've been over a lot, right? And it kind of makes sense. The smaller the wavelength of the light, the less it's going to like bend around your detector. And so you can maybe discern smaller and smaller things. The bigger the detector, the smaller the thing you can discern. That's why the detector is in the denominator, the wavelength is in the numerator. Okay? So suppose we go for like radio wavelengths like millimeters wavelength. So it's not it's not quite radio, it's like millimeter. So it's it's um it's like shortwave radio. Okay.

21:24So about like 1.3 millimeters. Um and I'll get into why we want to do radio and not optical which is at the hundreds of nanometers, right? Um so suppose we