 Hi, I'm Zor. Welcome to Unizor Education. We continue talking about units of measurements in physics. Primarily, we are talking right now about base units in the international system of units called C. So today we will talk about brightness and how to measure it. This lecture is part of the course called Physics for Teens, presented on Unizor.com. I suggest you to watch this lecture from the website. You might have found it somewhere else on YouTube, for example. The website thisunizor.com is preferable because every lecture has a textual part. It's like a textbook, so you can watch the lecture and you can read basically the same thing in kind of a written textbook-like format. The website is logically arranged, obviously. It's the course, which means there are something which we have to talk about first, and then based on this we talk about next, next, etc. So there is a logical sequence and there is obviously a menu, hierarchical menu, which drives the whole course. There are problems. There are exams in the course. So it's preferable to take the course, basically. The website. Now there is a prerequisite course in the same website. It's called Math for Teens and you definitely have to know your math before studying physics. By the way, the website is totally free and there are no advertisements, just pure knowledge for your consumption. Okay, now. So we're talking about brightness and how to measure it. Well, it's kind of a difficult subject because the brightness depends on so many different factors, including subjective factors like the sensitivity of our eyes. So physicists were kind of struggling with this particular issue and what I will present right now is some kind of analysis of how they were thinking about to measure the brightness prior to basically saying how the system, the C, is measuring it right now. Okay? So it's from relatively simple beginning, how can we actually go to the rather complicated ending of measuring the brightness? Okay, so let's start with relatively simple concept which we understand. Now, what is light? Light is electromagnetic oscillations and we were talking about what kind of energy electromagnetic waves actually carrying. Now this is all in a previous lecture and by the way, this is why I'm talking about you have to take the course because right now I'm just using something which have been covered before. So electromagnetic waves carry energy and basically we know what kind of energy it is how to measure it, etc. So the first concept which I would like to talk about is something which is called radiant radiant radiant flux, but then basically radiant flux is amount of energy, any particular source of light in its per second, per unit of time, which is second. So it's energy which is measured in watts in C and time is measured in seconds. So it's basically in joules. This is just pure energy as physics, physicists understand it. Okay, so radiant flux is basically understandable what it is. It's just amount of energy which source of light in its per unit of time. Now next concept you remember we were talking about some subjective elements like sensitivity. Okay, so let's introduce the sensitivity to this. And this is called luminous luminous flux. Well, this is also amount of energy, but not exactly the same as radiant. There is a there is a very simple modification. Simple modification is sensitivity of our eyes. Yes, all our eyes are different. However, there are certain average sensitivity towards different waves, different wave lengths. Obviously, outside of the visible light the radiant flux would still exist, but luminous flux should not. So what physicists came up with is basically a function called luminosity function. So what is this? Well, if these are different wave lengths and this is sensitivity which is basically a factor. Maximum is at one. It's somewhere where the sensitivity, average sensitivity among different people is at maximum. It's about 550 nanometers, which is basically a green and the border was yellow. This is our sensitive, our sensitivity is at maximum these colors. And that's where it's equal to one. And then it goes down on both sides. And these are basically visible lights. This is ultraviolet, and this is not this is ultraviolet, not this is ultraviolet, less wave lengths and greater will be infrared, right? So basically that's the function which have been basically established as a luminous luminosity function. Actually, there are more than one functions because it depends on just general conditions. Maybe lighting or something else. But in any case, there is something which is called the standard luminosity function. And what it does, why not lambda? Lambda is the wavelength. So luminous flux is basically radiant flux times this function. So amount of energy emitted, if you multiply by this function, that would be the luminosity flux per unit of time, of course. Now, what if the source of light actually emits the light in many different wavelengths? Like for instance, sun has the whole spectrum from violet to red, right? So how can we deal with this? Well, we summarize. For each wavelength, we calculate this and we'll just summarize amount of energy which in this particular wavelength is emitted. Well, that's only if you have certain discrete wavelengths. What if it's a continuous wavelength from this to that? Well, obviously, we have to integrate. So if you have something like function which is called radiant flux, which is dependent on the wavelengths, this is radiant, which means it's pure energy per time. So you multiply it by this function y of lambda, which is luminosity function. And then you integrate it from zero to infinity for all kind of wavelengths. So this gives you the total luminosity function of this source of light. So basically, we have introduced radiant flux and luminous flux. Now, the unit of measurements of luminous flux, but it's not exactly the same as radiant because it's radiant times luminosity function, which reflects the sensitivity. So the unit is called then lumin. So this lumin is luminosity flux unit. Now, in theory, it's the same joules, the same unit of energy per time, but with the factor of luminosity function, which basically reduces the number for all different wavelengths except the maximum. Okay, so lumin is basically joule times this factor, which is called the luminosity function. It's dimensionless, but still we have a different unit of measurement. Now, this is not the unit of measurement of C. This is so far kind of an explanation. And I'm trying to gradually come to the concept of measurement of luminosity as it is in C right now. So we have introduced the lumin. All right. Now, lumin is basically a unit of measurement of the luminosity, luminous flux, which means it's all over the source of the light. Okay. How about the direction? Because sometimes the source of light can give uniform light to all directions, sometimes not. So we have to really introduce what is the brightness, if you wish, towards particular direction. Okay. Now, for this reason, we have basically a concept of the angle. But in this case, it's not the angle on the plane, it's the angle in space. And angles in space also can be measured. Now, remember that if you have an angle on a plane, what you do is you have a circle, right? And if this length of the arc is equal to one radius, then the angle is called one radius, right? Well, in three-dimensional world, we have a similar thing. It's called stereogen. Stereometric basically. Stereo-radium. Stereo-radium. Now, what is stereogen? But if you have a sphere and you have a cone, which basically cuts something from the surface of the sphere. Now, if the area is one R square, where R is the radius, then this solid angle, which is inside the cone, is measured as one stereogen. Okay. It's kind of similar to plane geometry. And that's how we measure solid angles. It's like a cone. The question is what is the area? By the way, the area of the whole sphere is 4 pi R square, if you remember. Now, similarly, in the two-dimensional world, the length is equal to 2 pi R, right? So, which means in the full angle, we have 2 pi radians. In this full solid angle, we have 4 pi stereogen, okay? So, stereogen is a measurement of the angle. And what I would like to say is that the new unit is can't candela. It's basically lumens per stereogen. So, if you have the total amount of basically energy emitted per second and we divide it by angle, that's a per unit of angle, so to speak. What's going on over there? Okay. So, if you have total amount of energy per second, you divide it per angle, where it's actually distributed, you will get the brightness in that particular direction. So, that's what's important. Okay. Now, this is all analysis. I'm just trying to gradually bring you to the concept of candela. Now, it's kind of difficult because you brought everything into this variable, which is amount of energy, direction and sensitivity. Too many different factors are contributing into this particular unit of measurement of brightness. Now, how was it basically measured before? In the very beginning, one candle made of a specific composition, whatever the candles are made of, of specific form or specific weight, was about a one candle. I mean, it was distributing the light which was considered in any direction as one candela. That was kind of a beginning of introducing the brightness as a measurement of the brightness. So, they were saying that the brightness of one particular candle of specific kind of composition in a specific direction would be one candela. Well, obviously it was not perfect. I mean, candles, that was a long time ago. Well, then they decided to do it a little bit more scientifically. So, they were saying, okay, let's take platinum, melt it, and when it's melting, it's actually emits certain amount of light melting platinum. So, amount of light, which is emitted by one square centimeter of melting platinum, the temperature should be really right where it starts melting or starts freezing. Melted platinum starts solidifying or solid platinum starts melting this particular temperature, temperature of melting. Whatever the light is emitted from melting platinum, and then they divided it by 60, would be one candela, an abbreviation of candela CD. Now, why did it divided by 160? Well, to bring it into correspondence with candles. So, the new candela would be basically the same as the old candela. Old candela is the brightness of a candle. New candela is the brightness of melting platinum, but to basically equalize them, they put one centimeter of the surface of the platinum melting platinum and divided by 60. The brightness amount of energy basically divided by 60. Now, this is also not perfect because, again, there is a sensitivity of the eye, et cetera, et cetera. So, what was next? Well, next, physicists decided to be precise. Now, how to be precise? Well, first of all, to be precise, they should really get rid of polychromatic light. They should go to monochromatic because it actually is something much more precise. And they have chosen the wavelengths which corresponds to maximum intensity, maximum sensitivity, excuse me, of the eye, which is 540 times 10 to 12 hertz, which is about 550 nanometers wavelength. So, this is the frequency, this is the wavelengths. And this is basically the greenish-yellowish kind of a color which our eye is the most sensitive to. And that's where the luminosity function, remember, it has the peak where it's equal to one. So, we don't really have to get this luminosity function into account for this particular wavelengths. So, for this light, they have decided monochromatic light. Okay. So, then, they decided to have this particular light. And they have divided it by 6, 1, 6, 83 joules per steradian. So, again, joules is amount of energy per second divided by steradian because we are talking about one particular direction. So, the amount of light of this particular light, which is equal to 1, 6, 683 of one joule per steradian, is called one candela. By definition. So, now, you see, we are, before we kind of came up with the concept of candela, starting from the radiant flux and then luminous flux, etc., etc., divided it into steradian and gut candela. Now, we have decided to do it more precise. And we have decided that one candela means certain amount of energy, means this amount of energy per unit of time, per unit of solid angle would be, by definition, one candela. It does not involve any other wavelengths but this one. So, if this amount, if this light of this particular frequency, this particular wavelength, emits this particular amount of energy per unit of time, per unit of solid angle, then this is the light which we consider to be one candela. From which we come up with lumin as a unit, which is candela times steradian. So, if it's one candela in one steradian, that will produce amount of luminous flux equals to one lumin, which is basically energy per unit of time, joules. Now, it's lumin because now we can introduce the luminosity function and we can multiply it by whatever the brightness of this particular source of light is to get to any other particular wavelengths. So, that would be kind of a scale which we are using to measure the brightness of all other, yes, then we will introduce this luminous function. But it's not part of the standard, so to speak. Standard is to define candela using only this particular light and if it's emitting this particular amount of energy per second, per solid angle. So, that's the definition of candela and from candela we go to luminous flux, etc. And as at the conclusion of this lecture, I'll just give you a concrete example of how much lumens are produced by certain devices which you have. Now, if we would like to have 800 lumens output, that's what 60 watt incandescent lamp gives. That is about 14 watts fluorescent and about 10 watts of LED lamp. So, all in these they consume different amount of energy to produce this amount of light, basically. So, you see, this is consumption of energy, this is output energy, output of electromagnetic oscillations produced by this particular source of light. So, this incandescent, fluorescent and LED. And also, if, for example, you have a source of light of one candela and it's uniform in all directions, then how much lumens does it produce? If we're talking about only the light of one candela, we have to multiply it by how many star regions are in the sphere, right? Which means 4 pi. So, it's 4 pi lumens. So, one candela, this is the source of light which produces the brightness of this light is one candela, which means one joule per second per star region. Then you multiply by a number of star regions in the sphere and that's how much lumens it produces throughout the whole space in all directions. But only if it's uniform. Now, what if it's not uniform? I mean, you can think about certain sources of light which are not uniformly distributing light in all directions. Well, you have to integrate as usual. But let's not talk about this. It's kind of a rare stuff. Okay, so my purpose was to explain how physicists are measuring the brightness. Was it necessary to introduce this candela as a base unit in C? Well, quite frankly no, because it's derived from joules, from seconds and from star regions. But for whatever reason, they have decided to basically call it one of the base units and instead of derived units. And that concludes basically my base units in C explanation. Now, I will talk next lectures, I will talk about derived units. And obviously there are derived units. Yeah, I mean, the same joules actually is also derived units, for instance, right? So base units are finished. We will, next lecture, we will start derived units. Meanwhile, I suggest you to read the notes for this lecture. So basically that's it. Thank you very much and good luck.