An object is struck by a beam of white light containing all the colours of the spectrum, as shown in the diagram. Some colours are reflected from the object and some are transmitted through the object. Assume that all the colours of the light in the beam contain the same amount of energy as each other.
Now, before we move on to the next bit, let’s read through this paragraph again to pick up any information that we can. So we know that we’ve got an object struck by a beam of white light containing all the colours of the spectrum. This we can see that’s shown to us in the diagram. We can also see that some of the colours are reflected by the object and some of the colours are transmitted through. We’ve also been told to assume that all the colours of light in the beam contained the same amount of energy as each other. This is important. We’ll come back to this very soon.
Now, let’s read what the first part of the question wants us to do. We’re asked, what percentage of the energy in the incident light ray does the object reflect? Answer to one decimal place.
So we know that we’ve got seven colours in the spectrum: red, orange, yellow, green, blue, indigo, and violet. We also know that each one of these colours contain the same amount of energy as each other in this particular beam of white light. So we need to look at which of the colours are reflected by the object. In this case, orange and blue are both reflected by the object.
This means that when we put in a beam of white light, which contains seven colours, two of them are reflected back. And since each one of these colours has the same amount of energy, we therefore know that two-sevenths of the energy we put in is reflected back at us.
However, we don’t just want a fraction. We actually want a percentage. This is what we’re asked to find in the question. So all we need to do is to take our fraction two-sevenths and multiply it by 100 percent in order to give us a percentage. We can plug this into our calculator and this gives us 28.5714 dot dot dot percent.
However, that’s not our final answer. Remember that we’ve been asked to answer to one decimal place. So here is our first decimal place. It’s the one after that, the second decimal place, that would tell us whether the first one rounds up or stays the same. In this case, the second decimal place is a seven. That number is greater than five. Therefore, the first decimal place will round up. So the 28.57 dot dot dot percent rounds up to 28.6 percent to one decimal place. And so our answer to this part of the question is that 28.6 percent of the light is reflected to one decimal place.
This means we can move on to the next part of the question. This part of the question is almost identical to the previous one. However, it’s asking us, what percentage of the energy in the incident light rate does the object absorb? Not reflect, but this time we’re looking for how much it absorbs. Again, we have to answer to one decimal place. So we know that two-sevenths of the energy is reflected and two-sevenths is transmitted. The rest of it therefore must be absorbed by the object.
In order to work out how much is absorbed, we need to do the following: we’ve got an entire beam of light initially. So we can say that that’s equal to one. Then, we’ll lose two-sevenths of it because two-sevenths is reflected. So we subtract two-sevenths from one and we also lose another two-sevenths as transmission. So another two-sevenths get subtracted, which means that this value whatever remains is how much is absorbed by the object.
We can replace the one with seven-sevenths because seven divided by seven is one. And since all the denominators are the same, the numerators become very easy to handle. We’ve got seven minus two minus two. That happens to be three and the denominator is still seven. That means that three-sevenths is absorbed, two-sevenths is reflected, and two-sevenths is transmitted.
So because we’re being asked how much is absorbed, we need to work out three-sevenths as a percentage. Once again, we work out three divided by seven times 100 percent, which ends up being 42.857143 dot dot dot percent. But once again, we need to work out to one decimal place. So here is the first decimal place and here’s the next one, which will tell us what happens to the first one.
This second decimal place is a five, which means that is greater than or equal to five. And therefore, the first decimal place will round up. And so we’re left with 42.9 percent. And therefore, we can say that 42.9 percent of the energy is absorbed to one decimal place.
Moving on, there are two more parts in this question that we need to go through. So let’s look at the first of those two: what colour will an object that emits only red, orange, and yellow light appear if viewed through the shown object? So in this case, we’ve got an object that emits only red, orange, and yellow light. And we are viewing this object through the object that we’ve been discussing in the question so far.
So let’s say that we’ve got this emitting object somewhere around here and it only emits red, orange, and yellow. In other words, it doesn’t emit green, doesn’t emit blue, doesn’t emit indigo or violet. So we can cancel all of these ones out. Now, let’s see what happens when we view this object that is emitting red, orange, and yellow light through the original object in the question.
So this on the left is our little eyeball and we need to work out which of the colours we’ll end up seeing. Now, we also need to correct in our diagram what’s happening on the reflected side of the object and the transmitted side. Because the only inputs are red, orange, and yellow light, so this blue light doesn’t exist because we’re not putting any blue light into the object in the first place. Similarly, this indigo has to go, which means that when we put in red light, this object transmits that red light. We can see this here.
Similarly, we put in orange light and that orange light gets reflected. We see that here. Finally, we put in yellow light and it’s neither being reflected nor transmitted. So it must be being absorbed. So if we’re looking from where we’ve drawn our little eye — that is if we’re looking at the transmitted side of the object — then the object that’s emitting the light, this one here, will appear to be red because all of the orange and yellow components are not being transmitted. And so our answer to this part of the question is that the object that’s emitting light will appear red.
Moving on to the final part of the question, this bit is asking us what colour will an object that emits only red, orange, and yellow light appear if viewed reflected from the object. So this time, our eye is not on the left side of the diagram, but rather we’re viewing from the right. And as we’ve discussed earlier, when we put in red, orange, and yellow light, the object here transmits the red, absorbs the yellow, and reflects the orange. Therefore, we’ll only see the orange light coming back at us and the object emitting the light will appear orange to us.
Finally, we’ve reached the end of the question.