In this video, we’re talking about colours of light. And the first thing to know about these colours is that they exist. Not only do our eyes tell us this everyday, but if we take white light — shown here — and send it into a bit of glass — known as a prism — then on the other side of that prism, we’ll see the individual colours that make up white light all spread out.
Colours of light come from the fact that our eyes respond differently to different wavelengths of light. If we look up at the sun in the middle of a clear summer day — don’t do this for long by the way — but if we do, the sun will look white. Whenever we see white light, that means that all the colours our eyes are sensitive to are present. But of course as we look out at a natural scene, most of the light we see is not white; it has a particular colour to it. For example, the sky looks blue to our eyes, grass appears to be the colour green, and perhaps we see a flower that looks yellow in colour. All these individual colours we’re seeing are contained within the white light that comes from the sun. But clearly, there’s been some sort of selection process so that we only see a particular colour when we look at a particular object.
All this has to do with the fact that whenever a light ray — say a ray of white light — is incident on an object, there are a number of things that can happen to that light. One thing that can happen is that the ray of light is reflected from the object. Another thing that can happen is that it’s transmitted or goes through the object. And the third thing that can happen is that the light goes into the object but never makes it through. In other words, it’s absorbed. In any given interaction like this, how much light is reflected or transmitted or absorbed varies with the material. Interestingly, this series of interactions is behind all the colours we perceive in the blue sky, the green grass, and the yellow flower.
To see this a bit more clearly, let’s look at the interaction of sunlight with grass in more detail. If we have a clump of grass that sunlight is shining on, that is white light containing all the colours of the rainbow, then we can represent that light based on the individual colours it’s made up of. By the way, there are more colours in visible light than the four we’ve shown here. But this is just a given idea. So anyway, all these different colours of light that make up white light are running into this clump of grass. And for each individual colour, the grass either reflects it, transmits it, or absorbs it.
Now, if we looked at this clump of grass, what kind of light would our eyes see? Well, we wouldn’t see any of the light that the grass absorbs because that stays within the grass. And we wouldn’t see any of the light that it transmits that goes through the grass. Our eye would only see any colours of light that the grass reflects. And of course, we know what that colour predominantly is. It’s green, which tells us that in the case of grass with all these other colours with the reds, with the blues, and with the yellows, those get absorbed by this material or transmitted through it. It’s only green-coloured light that bounces off the grass and comes to our eye. And since every time we look at grass it looks green, we say the grass is green, even though actually this is the colour that’s being reflected by that material.
This is the same thing that happens by the way with that yellow flower we mentioned. When white light hits the flower, that is light of all different colours, it’s the yellow light predominantly that gets reflected or bounces off of the flower. And the other colours, the greens, the blues, and the reds, are either absorbed or transmitted. This points to the interesting fact that the colour of any particular object we see is actually only being reflected by that object. So in some sense, the object is not that colour.
But anyway, the important point here is that whenever light interacts with an object, one of three things can happen to the light. It will either be absorbed by the object, transmitted through it, or reflected off from it. And it’s that reflected light that our eyes are able to see when we look at the object. Building off that, if we look at an object and the object appears white, say a white automobile or a white T-shirt, that means that all the colours of the rainbow are being reflected by that object. It’s not absorbing any of them.
On the other hand, if an object is coloured black or looks black to our eye, that means it’s absorbing all the wavelengths of light incident on it and none of them are being reflected. By the way, this is related to the fact that if you wanna stay cool on a hot summer day, it’s better to wear light-colored clothing than dark. While a white material is one which reflects all the colours of light which hit it, therefore absorbing none and heating up very little, a black material is one that does the opposite. It doesn’t reflect any light, but absorbs it all. Therefore, it heats up at a much higher rate than a whiter material.
Now, we’ve said that white light that comes from the sun can be spread out so that all the individual colours that make up that light are visible. If we were to see all those colours as a continuum, it would look something like this. This is known as the visible spectrum because it contains all the types of light that our eyes are sensitive to that our eyes can see. It’s not the only sort of light that exists. But for all the light that’s outside the spectrum, our eyes just don’t notice it. We can see in this spectrum that there’s a whole range of colours, starting at red on the left side and getting to violet on the right side.
Roughly speaking, the main colours that our eyes pick out in this spectrum going from left to right are red, we’ll abbreviate it R, orange abbreviated O, yellow abbreviated Y, green abbreviated G, then blue B, indigo I, and violet V. So we have this somewhat unmelodious acronym, ROYGBIV, that helps us remember the main colours in the visible spectrum. One interesting fact about these different colours in the visible spectrum is that there’s a mathematical way to tell them apart. Now, this is actually really helpful because if we pick out any particular spot on the visible spectrum, say that spot there, and we try to identify the colour at that spot, well, we can get into different names and different perceptions of colour and different descriptions of colour if there wasn’t a quantitative way of saying where that part of the spectrum is.
But thankfully, there is a quantitative way to describe precisely any point on this visible spectrum. And that method is to use what’s called the wavelength of a colour of light. This is a measure of the distance along the wave’s direction that covers one complete wave cycle. So, for example, say we had some yellow light. Well, one wavelength of that yellow light would be equal to this distance, one complete wave cycle along the wave’s direction. Often, for shorthand, the wavelength of a wave is symbolized using the Greek letter lowercase 𝜆. This yellow light has a particular wavelength. And we can call it 𝜆 sub 𝑦.
Now, if we were to compare this wavelength of yellow light with a wavelength of green light, we would see that the two are not the same; the wavelength of green light is shorter. And if we were looking at a wavelength of blue light, then that would be shorter still than green or yellow. As we move across the visible spectrum, there’s a trend. When we go from left to right, that is when we go from red towards the violet end, the wavelengths of the colours of light get shorter and shorter. And when we go the opposite direction towards the red end of the spectrum, then the wavelengths get longer.
When we talk about the wavelengths at the very ends of the spectrum, things get a bit interesting because remember this is called the visible spectrum. This means that if our eyes can see a colour, that is in the visible spectrum. But not all human eyes are the same and not all sensitivities to light are quite the same. Despite those small differences, there are accepted average values for the wavelengths of either end of the spectrum, red light and violet light. White at the red end the spectrum has a commonly accepted wavelength of 700 nanometres.
Now, a nanometre is equal to one-one billionth of a metre. So what we’re saying is that red light has a wavelength of 700 billionths of a metre. So that’s pretty short. But as it turns out, the wavelength of violet light is even shorter. A commonly accepted average value for violet light is 400 nanometres or 400 billionths of metre. And just as we can identify the red and violet colours of the spectrum by specific wavelengths, so we can identify the other colours. For example, green light is known to have a wavelength of approximately 550 nanometres.
This wavelength measurement scale that we’re talking about for the visible spectrum means that we can quantitatively identify any particular spot on that spectrum. We could specify say a wavelength of 476.325 nanometres and based on that number could find that exact spot and therefore the corresponding colour on the visible spectrum. Now that we have a bit of a sense for what the colours of light mean and how those colours interact with objects, let’s get some practice through an example.
A light ray that strikes an object is partly reflected and partly transmitted, as shown in the diagram. What percentage of the light ray’s energy is absorbed by the object?
Taking a look at our diagram, we see our object, this box here, and then light is coming in to the object from the right. We see that some of the light 15 percent makes it all the way through and it’s transmitted and 35 percent is reflected back. The question asks us how much of the light ray’s energy is absorbed by the object. To start figuring this out, let’s recall the ways that light can interact with an object that it’s incident on.
When light hits an object, there’re only one of three things that can happen: the light can be transmitted, reflected, or it’s absorbed by the object. This means that for any interaction between light and an object, if we add up all the light that’s transmitted, reflected, and absorbed, then we’ll get the total light that was incident on the object in the first place. We could write it this way as an equation. We could say that the total light in incident on an object is equal to the light reflected plus the amount transmitted plus the amount absorbed.
Now, in our scenario, we have some amount of light in; we don’t know what that is. But we do know what percentage of that light is transmitted and what percentage is reflected. Going to our equation then, we can replace Trans, the amount transmitted, with 15 percent. And then we can replace reflected with 35 percent of the amount of light that comes in. So we have that the total amount of light incident on our object is equal to 35 percent of that amount plus 15 percent of that amount plus the amount of light absorbed. If we add together 35 percent and 15 percent, we get 50 percent.
So 50 percent of the incident light plus the amount that’s absorbed by the object is equal to the total incident light. This tells us that 50 percent or half of the light incident is being absorbed by this object. If we add that percentage to the percentage that are reflected and transmitted, we get 100 percent. So we know that 50 percent of the incident light ray’s energy is absorbed by this object. Let’s look at a second example involving the colours of light.
What colour is a beam of originally white light after the beam is both transmitted through object B and then reflected from object A?
Looking at our diagram for this problem, we see these two objects, object B and object A. Both of these objects have all these different colours red, orange, yellow, green, blue, indigo, and violet incident on them. The fact that those specific seven colours are being used tells us that white light is being shine on these two objects; that is light that contains all the colours of the visible spectrum. But we see as we look at the diagram that object A and object B respond differently to these colours.
For example, looking at object A, we see that it reflects three of these seven colours. It reflects red light, yellow light, and blue light. For object B on the other hand, we don’t see what colours it reflects, but what colours it transmits. Object B transmits green light, blue light, indigo light, and violet light. Based on the diagram, we can say that all the other colours of light that reach object B are absorbed by it. And that brings us back to our question. If white light, that is light with these seven colours red, orange, yellow, green, blue, indigo, and violet is transmitted through object B and then reflected from object A, what colour or colours will remain?
Here’s how we could think of it. Say that we have object B in front of object A and we shine white light at an angle on object B. Some light will make it through that has be transmitted through object B and then afterwards running to object A and be reflected off of it. It’s that light in particular the colour of that light that we want to solve for. To answer that question, we’ll need to know what are the colours of light that are transmitted through object B and then what are the colours of light reflected from object A.
Our diagram helps us answer this question. We know that object B transmits four colours of the original seven. It transmits green light, blue light, indigo light, and violet light. So at this point in the light’s journey after it’s made it through object B, there are four remaining colours, these four we’ve just named. Then, these four colours run into object A. And we want to see which colours if any are reflected. Again, our diagram will help us. We saw that object A reflects light of three different colours. It reflects red light, yellow light, and blue light. Now, in this case, the red and yellow don’t matter much because no red or yellow light is actually reaching object A in the first place. Those colours have been filtered out by object B. But blue light is among the list of colours that reach object A.
So of the green, blue, indigo, and violet light that reach object A, only blue is gonna be reflected. Green, indigo, and violet will be absorbed as we see in the diagram. Because blue light is the only colour of light that’s both transmitted by object B and reflected by object A, we know that that is the answer to our question. It’s blue light that will be reflected from object A after this white light has been transmitted through object B.
Let’s summarize now what we’ve learned about colours of light. Starting off, in this lesson, we saw that our eyes are sensitive to a range of kinds of light, which we perceive as different colours of light. We learned that all the colours of light that we see are contained in white light. We saw that when light hits an object, it can do one of three things: it can be absorbed, reflected, or transmitted through the object. Furthermore, it’s the case that light we can see is part of what’s called the “visible spectrum.” This spectrum ranges from 700 nanometres to 400 nanometres in wavelength. Lastly, we saw that the main colours in this spectrum can be remembered using the acronym “ROYGBIV,” red, orange, yellow, green, blue, indigo, violet and that the wavelengths of each of these colours or any particular colour on the visible spectrum can be identified using a specific numerical wavelength value.