An astronomer looks at the sky with her naked eye and sees the stars shown in the diagram. If the astronomer uses a telescope to look at these stars, which of the following diagrams correctly represents what she would see?
So here we can see the astronomer’s view when she just looks at the sky with her naked eye. And we can see that there are four stars in view, each of a different color. We need to decide which one of these five diagrams correctly shows what the astronomer would see if she looked at the same stars but through a telescope. To answer this question, let’s look at each option in order and see if they show what we might see if we looked at this view through a telescope.
So, let’s start with option (A). We can see in this diagram that the distances shown between the stars have actually decreased. So, the stars look closer together than they do with the naked eye. In addition, each of the stars in diagram (A) is the same size as it was when the astronomer looked to the sky with her naked eye. For example, the yellow star in the middle of this diagram is the same size as the yellow star in the middle of this diagram. Telescopes are used by astronomers to give them an enlarged view of distant objects, whereas in option (A), the objects have been kept the same size, and the distances between them have just been decreased. Which isn’t actually something a telescope can do. So, option (A) can’t be the correct answer.
Option (B) shows us an enlarged version of the stars, so it seems like this is a good option. After all, like we just said, telescopes are used to give an enlarged view of faraway objects. However, it’s important to note that when we use a telescope to enlarge our view of an object, that it will also enlarge the apparent distances between objects. So, while the telescope will make individual stars appear bigger, it will also make them appear further away from each other. Option (B), however, shows us an image where each of the stars has grown in size, but the distances between them are exactly the same. Since this isn’t how image magnification works in a telescope, we know that option (B) is not the correct answer either.
If we look at option (C), we can see that, again, this image has changed the individual sizes of stars. But it hasn’t actually changed their positions relative to each other. So, we know that this isn’t the correct answer either. In addition, we can see that the sizes of the stars in this diagram have changed by different amounts. For example, the yellow star in the middle of diagram (C) remains roughly the same size as when it was seen with the naked eye. But the white star at the upper left has grown bigger. Telescopes will magnify an image uniformly, meaning that they won’t change the sizes of different parts of the image by different amounts, which is another reason that tells us (C) is not the correct answer.
Once again, option (D) shows us an image where different parts have been enlarged by different amounts. So, in this case, all of the stars have kept the same positions but the yellow star in the middle has been enlarged. We know this isn’t how telescopes work. If we wanted to get an enlarged image of the star in the middle, then we’d also end up getting enlarged images of the other stars. And the distances between these images would increase. So, option (D) is not the correct answer either.
This only leaves us with one option, but this is the only option where we can’t see all of the stars. To explain why this is, let’s think about exactly how this image would be magnified by a telescope. We can see that in diagram (E), the apparent size of the yellow star in the middle has increased. In fact, the diameter of the image of the star shown in diagram (E) is roughly five times the diameter that the astronomer saw when she looked at the star with her naked eye. In other words, we can say that the image of this star has been magnified by roughly five times.
Now, if we had a telescope that magnified the diameter of this star by five times, then it would magnify all of the different distances we could see with the naked eye by five times. That means that the distances between the stars would also be magnified by five times as well, which would make them appear five times as far apart. And if that’s the case, then the other stars wouldn’t fit within the image produced by the telescope. In fact, relative to the position of the magnified yellow star, we would expect the magnified images of the other stars to be roughly these sizes and positions. So, option (E) is the correct answer. This is what the astronomer would see if she looked through a telescope.