13.3 Speed of Light

Ok, today we're gonna look at the speed of light. We've already realized that the speed of light is 3 times 10 to the 8th when you're doing calculations, but today we're going to figure out how they actually measured that and how that sort of changed over the years as well. So, the first one we're gonna look at is when I go back to Galileo times. Galileo is sort of the first documented case of trying to calculate the speed of light. So, what he did is basically he went up on a tall hill, he sent his lab assistants on another tall hill, and he said he's gonna open his lantern and told his assistant that as soon as he sees the light, he wants the assistant to open his lantern. Then Galileo just said, "If I know the distance between us on this picture that's at the bottom, we have one kilometer apart," he says, "if I know the distance, all I have to do is measure the time that it takes for me to see the light." Light, when he saw the measure, the time takes from when he opens his lantern to when he sees his other guy's lantern, and then he knows that he measured double the time. So, you two the total distance, and then he would basically divide it by 2, times whatever time he measured between the two. But because he had lanterns which weren't very accurate, plus he only had like pretty poor to watch back in them days, to calculate the time, he never got a very good answer. And he even realized, he said, that this is likely not very accurate because it relies too much on human reaction time. So basically, what he probably measured was just how quick he responded to seeing the light later on. So, we're talking about 75 years or so later, astronomer holy Romer from Holland. He actually noticed as he was checking out planets and moons. Things like that, he noticed that on certain days there was a delay when he would see Jupiter eclipse one of its moons. So, at certain points of the year, let's suppose in July, he noticed that it was occurring at one o'clock. But later on in the year, in January, it was happening at 1:30 or something like that. So, what he kind of proposed then is, we know that our distances are changing. In this little map, if Earth is the green one and Jupiter is the orange one, when they're close together, we have a closer distance. But later in the year, you can see the distance would be quite a bit larger. So, Romer figured out that the time delay that we were getting with the eclipses were actually due to the travel distance the light had to travel to reach us. They had some rough ideas of how the distances were between the Sun And the earth, the sun, Jupiter, and so on. So, we used those rough numbers and did some calculations to get a fairly reasonable speed of light. Once again, heat is basically the distance over time. He just measured what the time delay was, and he knew the distance change. From there, he could figure out what the velocity of light was. Based on today's results, he was quite a bit off, but it was actually the first attempt to measure the speed of light that came up with a reasonable answer. Later on, we're now in the mid-1800s. There are two scientists, and one happened after the other. But these are sort of the first cases where we actually get pretty reasonable numbers. A scientist named Forzou actually came up with a pretty good way. What he did was he basically just took a gear, so imagine. Sort of like the cogs on a gear, kind of like little wheels and so on. What he did was shine a light so that it would pass through the spaces on a gear. Then he would spin the gear, and the idea was that the light would pass through a space on the gear, hit a mirror, and reflect back. He set up the mirror at quite a long distance, even half a kilometer away. They wanted a large distance because they knew light was traveling really fast, and having a bigger distance would give them more time to work with. He would shine the light, it would go through the space on the gear, hit the mirror, and come back. Then he would change the frequency or rotation of the gear so that it would just turn one cog to allow the light to go through. If you imagined the Gear spins, let me just erase the sphere a bit. So, if the light's traveling and it goes through the space of the gear, and the gear rotates one tooth, the light would go through this cog. And then, when it hits the MIR and reflects, it would actually come back through the next cog as it rotates. All he would do is figure out the time it took for the cog to spin one turn, and then he used that time to figure out the actual speed of light based on the distance it had traveled and the time it took to spin. He actually got a pretty good answer, so he was only about five percent off from what we accepted. A fork actually took Zoe's method and refined it a little bit, but instead of using a gear spinning, he used the... Spinning year, so the idea was the same sort of thing. The light would hit a mirror, and he set these up at angles. So, he had this mirror that was spinning. It would hit the mirror, bounce off, and go. He set it up even further, thinking that larger distances would be even better. So, he bounced it off another stationary mirror 35 kilometers away. Then, it came back again. He made it so that he knew the spinning of the mirror. But when it came back, if the mirror was turned a little bit, let's sort of imagine the mirrors that are angled to start with, but after the light bounces back, it's now going to be at a bit of a different angle. This would then reflect the light back at a little bit of a different angle again. So, he would just measure the angle. He knew that if he could figure out the time it took to spin the mirror to. Change that certain degree of angle, and he could use that time to figure out the distance. I had the time to calculate our speed, and he actually came up with a pretty solid answer that was pretty close to Fizzles, but a little bit easier to do and a little bit better answered. The key was then Albert Nicholson. So, this is in the late 1800s. Nicholson used Fizzles' idea, but he used better quality mirrors. Instead of just having one mirror rotating and measuring the angle, he decided to use an octagon mirror or an eight-sided mirror. He got really good results. He would take the light, shine it, it would hit the mirror, bounce off to another mirror that was 35 plumbers' wayne, bounce back, and then he would see it through his telescope. What he did was he figured out that if we could rotate the mirror so that if... The NIR rotated at the right speed where it only turned exactly 1/8 of a turn. Then he would be able to see the light. If the mirror is going too fast where it turned too much, the angle would be off and the light would get bounced off. It went Solon off and light might go the other way and so on. So all you have to do basically is you get the mirror to rotate at the right speed. And once he did that, then he could get the proper population. So let's actually do one of his calculations. This one says we have a curved mirror 35 kilometers away. And he found that they get to spin the eight-sided mirror at 32,000 rpms. So the question we're gonna do is what is the speed of light based on that information if we know, let's cool their formulas. We know that our velocity is going to be distance divided by time. So the first thing is how do we calculate the. Distance: While we're assuming that the light and the telescope are right near the mirror, so we're basically just dealing with a distance of 35 kilometers. However, it's going to the curve near and then back again, so we actually have a total distance of 70 kilometers, or 70 thousand meters. That's going to be our distance. Now, we just need to figure out the time. If we know that the eight-sided mirror spins at 3200 RPM, what we want to do is figure out what that is in terms of time. So, 3200 revolutions per minute, or RPM. We want to convert that to seconds. 3200 is the number of turns in a minute, so if we divide that by 60... That'll actually give us per second. So 3200 divided by 60 gives us 533 Hertz (or per second). So then, what we wanted is actually at times. Remember, time is one over frequency. So we'd have 1 divided by 533, which gives us an answer of 1.87 times ten to the negative three seconds. So all we have to do then is perform that one little trick. Remember, that's the time for one whole revolution. We only want this to go one-eighth of a turn, so we actually have to divide that by eight as well. This ends up getting us 2.34 times ten to the negative four seconds. So that's the number that Nicholson would put in the formula — 2.34 times ten to the negative four. So, 70,000 meters takes 2.34 times ten to the negative four seconds. We divide those out, and we don't growl about decimals or keep things fairly close, we actually get about two point nine eight six times ten to the eighth meters per second, which is pretty close. We accept an answer of 3 to the 8th, and we're getting those kind of numbers. So, what happened is Nicholson kept doing this over and over again to try to get better results. He changed his distances and his mirrors to be a little bit better quality. And he basically, after several reprises, he's the one that came up with the three times ten to the eighth number that we still use today. This is in the early 1900s, and in 1907 he actually got the Nobel Peace Prize for his accurate calculations. And to this day, we still use his method to calculate the speed of light. The most accurate that's ever been measured to date is pretty close to what he calculated, and you can see we're. [Music] Just a bit under 3 to the 8th, you know 2.9979 roughly to the 8th. But if we round it off, we're still using the 3 times 10 to the 8th that Nicholson calculated. And that's it for this.