The data in table one was obtained from an investigation into the refraction of different colors of light at an air-to-glass boundary. The angle of incidence for each color of light was exactly 20 degrees. Describe an investigation that a student could complete in order to obtain similar data to that given in table one. The student uses the following apparatus: a ray box; a rectangular glass block; a set square; a tape measure; a pencil and large sheets of paper; a calculator that can automatically calculate the angles in a right-angled triangle using the ratios of the lengths of the triangle’s sides. The ray box has been set up for the student at the required angle of incidence. Your description should consider possible measurement inaccuracies. You may wish to draw a labelled diagram showing how the apparatus should be used.
Okay, so as we can clearly see here, this question is just a barrage of information. So what we need to do is to break it down into smaller chunks to try and make it more digestible. First of all, let’s have a look at table one here. Table one is a table that tells us the color of light and the angle of refraction. And as we’ve been told already, the data in table one was obtained from an investigation into the refraction of different colors of light at an air-to-glass boundary.
So here, we’ve got the colors red, green, blue, and violet colors of light. And we’ve also been given their angles of refraction. As well as this, we’ve been told that the angle of incidence for each color of light was exactly 20 degrees. Now, what we’ve been asked to do is to describe an investigation that a student could complete in order to obtain similar data to that given in table one. And we’ve been given the apparatus that the student is allowed to use. Also luckily for us, the ray box has already been set up for the student at the required angle of incidence, in this case, 20 degrees. That’s if we wanna match our experimental procedure to the experiment that gathered the data in table one. So let’s start putting some of this information together in a little diagram.
Firstly, we’re considering an air-to-glass boundary. So here’s our little glass block and this region is all air. Therefore, the air-to-glass boundary is this boundary over here. Also, because we’re looking at an air-to-glass boundary and not a glass-to-air boundary, the angle of incidence is gonna be on the air side and the angle of refraction is gonna be on the glass side. Now, we’ve been told that the ray box has been set up for the student already. And it’s been set up at the required angle of incidence. So this here is the angle of incidence. That’s the angle between the beam of light and the imaginary line, this dotted pink line that we’ve drawn here. That is the line that is normal to the boundary that we’re considering.
Now, in this case, it doesn’t actually matter what the angle of incidence is for two reasons. Firstly, we’ve been told that the ray box has been set up for the student already. And secondly, we’re only trying to obtain data that is similar to that given in table one. So regardless of what the angle of incidence is and how the ray box has been set up, we’re trying to find the angle of refraction. And what we’re going to be doing is to be changing the colors of light from the ray box and see how this angle of refraction changes based on what color of light we’re using.
So we wanna create our own table basically. We can call it table two cause we’re very original and imaginative. And in that table, we wanna have the color of light that’s coming out of the ray box that we’ve set up for our experiment and the angle of refraction that we measure. So the majority of this investigation that we’re going to be describing is going to consist of us accurately measuring this angle of refraction. Because it’s easy to change the color of light, we simply change it on the ray box. We can assume that the ray box can’t emit multiple different colors by using a filter or something like that. But in essence, we don’t really need to worry about the color of light column as much as we do about the angle of refraction column. Because we want to measure the angle of refraction as accurately as possible for different colors of light.
Now here’s the thing, we’ve just said that we want to try and measure our angle of refraction as accurately as possible. However, we’ve been told in the question that our description of our investigation should consider possible measurement inaccuracies. And we’ve also been told that we may wish to draw a labelled diagram. And this diagram will show how the apparatus should be used. So, let’s go about doing that.
Now remember, we’re limited in the equipment that we’re allowed to use. All we’ve got is a ray box, a rectangular glass block, a set square, tape measure, a pencil and some paper, and a calculator that will give us the angles in a right-angled triangle if we input the lengths of the triangle sides into the calculator. Now, we’ve already seen how the ray box has been set up as well as the glass block. And we’ve assumed that we can change the color of light coming out of the ray box. Maybe the ray box has some built-in filter attachment or something like that that can change the color of light coming out of it.
So if we wanna make our imaginatively-labelled table two, which has the color of light in one column and the angle of refraction in the other column, then changing the color of light is fairly simple. We just change it on the ray box. This means that the only thing we need to worry about is how to measure the angle of refraction. And to do this, all we can use is the equipment that we’ve been given.
Now, the first thing that we need to remember is that the angle of refraction is defined, we’ll call this 𝜃 sub 𝑟, as the angle between the beam of light in the refracting material and the line that is normal to the boundary. Now remember, we said earlier that this was the air-to-glass boundary. So this pink dotted line is normal to that because the angle between the pink line and the orange-dotted line is 90 degrees. And so, we’re trying to find the value of 𝜃 𝑟 for each color of light that we put through the glass block. And we’re doing this for a fixed angle of incidence, 𝜃 𝑖. Because we are told earlier that the ray box has been set up already and so 𝜃 𝑖 is fixed.
So how are we gonna go about finding the value of 𝜃 𝑖 if we don’t have a protractor? Problematic, right? Well, luckily for us, we’ve got a very special calculator that will give us the angles in a right-angled triangle if we tell it the lengths of the sides of the triangle. So what we need to do is to draw a right-angled triangle, where the angle that we’re looking for, this angle of refraction, is one of the angles of the triangle.
So what about this triangle here? One of the sides is this. This is the second side. And the third side is the beam of light. And we know it’s a right-angled triangle because this line is a normal to the surface of the glass block. And therefore, this angle over here is 90 degrees. So we’ve got our right-angled triangle. And now, what we need to do is to measure somehow this distance, this distance, and this distance.
Now, at this point, we come across a problem. This triangle is not exactly easy to draw or visualize. Because remember, in our experimental setup, all we’ve got so far is this beam of light going through our glass block. It’s all well and good talking about the normal line. But up until this point, it’s only an imaginary line. So we need to come up with a way of actually seeing this line. And we can visualize this if we actually draw the line in. So we need to place this whole setup on a large piece of paper which, remember, we have been given in this question.
Now remember, what we’re trying to do is to draw in this normal line. But even if we’ve placed the whole setup on a piece of paper, we can’t draw this line yet because the glass block is in the way. However, what we can do is to potentially draw the normal line in the other direction. And then, when we remove this glass block from the piece of paper, we can just extend this normal line in the other direction. Now, in order to draw the normal line in this direction, what we’re going to use is a set square.
Now, a set square is basically just a piece of plastic that is a right-angled triangle. And so, we’ll take our set square and we’ll take the corner which has the right angle on it and place that corner at the point at which the ray of light goes into the glass block. We can even place this line that’s part of the set square against the glass block surface. And then, once we’ve done that, we use our pencil to simply trace out the normal line to the surface.
So now that we’ve drawn this normal line in, when we remove the glass block, we’ll be able to extend it in the opposite direction. And so, we’ll be able to draw a dotted line in this region here. But here’s the thing, we have to remove the glass block to draw this line in the first place. But at that point, we don’t know how long to draw this line, right? So before we remove the glass block, we need to make markings on the page at this point, this point, and this point. That’s point number one, point number two, and point number three.
In fact, we can even get away with drawing dots just at point one and point three. Because the reason for this is that we could extend the normal line as long as we want once the glass block is removed. And we’ve got our points at point one and point three. And then, we could take our set square, place it like this such that this side of the set square is lined up with the normal line that we’ve drawn earlier and this side of the set square is lined up with the dot that we’ve drawn at point three. That way, we can then draw a line in this direction as well.
At which point, we’ve got the three corners of the triangle that we’re trying to measure. We’ve got point number one drawn on the paper already, point number three drawn on the paper already, and point number two which will be the intersection between the normal line and the line we just drew with the set square. Now, this is getting a bit messy. So let’s clarify this a little bit.
Let’s assume that we’ve only drawn this normal line, this point on point one, and this point on point three. Then, let’s switch off the ray box and move the glass block away from the paper. This is what we’d be left with: the normal line, the point at point one, and the point at point three. We can then use our set square to extend the normal line. And we can keep moving the set square until we end up extending the line quite far. But then, importantly, we get to the point where this edge of the set square is against the normal line that we’ve been drawing and this edge of the set square is against point number three.
At that point then, we draw a line along that edge of the set square. So now, what we have is this length over here, that starts at point number one and ends at the intersection between the orange and the pink line, and this length over here, that starts at the intersection between the orange and the pink line and ends at point number three. Finally, we can draw a line joining up point one and point three, erase everything else, and we’ve got our finished right-angled triangle. At this point, we can use the tape measure. And we can measure the lengths of this side, this side, and this side.
Once we’ve got those lengths, we plug in those values into our calculator. And the calculator will tell us the values of the angles in the triangle. We then take the value that corresponds to this angle over here, the angle between the pink and the green line, because that angle is the angle of refraction 𝜃 𝑟 that we’re trying to find. And then, once we’ve done that, we stick it into our table next to the color of light that we were using. So in this diagram, we started with green light. So we can say green in the color of light column. And then, we can say the angle of refraction whatever it ends up being in the angle calculator. Wohooo! We’ve got one of the readings on our table.
Now, we’ll repeat the whole thing after we change the color of light from the ray box to, let’s say, blue. So we put back our rectangular glass block, make a mark on point one and point three, and draw the normal line in this direction. Then, get rid of glass block, draw the normal line in the opposite direction, use the set square once again, find our triangle, measure the lengths of our new triangle, plug those lengths into a calculator, and find the angle of refraction for blue light. Then, we’ll be able to say blue in our column for the color of light and whatever the angle of refraction maybe for blue light.
Now, we keep doing this experiment until we’ve got all of the colors that we need and all of the angles of refraction. So that’s our description of the investigation that we would conduct.
Now remember, we were asked to consider possible measurement inaccuracies in our experiment. To do this, we need to zoom in a little bit to the setup. Specifically, let’s focus on where our ray of light enters and exits the glass block. We said that we were going to mark these points with a pencil on our piece of paper. Specifically, we called them point one and point three. But then, we need to realize that our beam is not going to be just a very very thin line. It’s going to have some sort of width to it. And this could be problematic. Because especially with a very sharp pencil, we would ideally mark the middle of the beam where the beam enters the block and the middle of the beam where the beam exists the block. Or, one edge of the beam and the other edge of the beam. And the reason we would want to do this is so that we get an accurate line from one point to the other, representing the actual direction that the beam is travelling in.
However, let’s say accidentally, we managed to mark this point at the entry point and this point of the beam at the exit point. Well then, the line that we’d end up drawing when we remove the glass block from the piece of paper would be this pink line over here, which doesn’t accurately reflect the direction that the ray of light was travelling in. Because the ray of light was travelling this way whereas the ray of light that we’ve drawn is travelling this way. And so, not quite the right direction. But then, the direction of this line is a problem. Because eventually, we’d end up wanting to measure this length here. And we’d instead end up measuring a very slightly different length. And this could be a potential source of inaccuracies in our experiment.
A consequence of this would be that we wouldn’t measure the angle of refraction that we’re trying to measure. Instead, we might end up measuring a slightly different angle which we would think is the correct angle of refraction. But it’s not, as a direct result of the inaccuracies in where we drew our two points. So the main point is that due to the thickness of the beam, due to the fact that it has some finite width, we might encounter some possible measurement inaccuracies. And so at this point, we’ve described the investigation that we would conduct and discussed a possible source of measurement inaccuracies. Therefore, we’ve reached the end of the question.