Video: Properties of Refracting Telescopes

A simple refracting telescope consists of two convex lenses of different focal lengths that are aligned along the same axis, as shown in the diagram. Which of the two lenses is more powerful? Which of the following statements most correctly describes the effect of a simple refracting telescope on the light that passes through it? [A] The light rays coming from the eyepiece lens are brought to a focal point. [B] The telescope makes parallel light rays from an object closer to each other. [C] The telescope produces an image that is larger than the imaged object. [D] The telescope makes parallel light rays from an object further apart from each other.

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Video Transcript

A simple refracting telescope consists of two convex lenses of different focal lengths that are aligned along the same axis as shown in the diagram.

Okay, so, in this diagram, we can see that we’ve got two lenses here, the objective lens and the eyepiece lens. And as well as this, we can see the object that’s being imaged and how the light rays from this object travel through the entire setup until we see them on the other side of the eyepiece. Now, the first question asks us, which of the two lenses is more powerful? And so, we need to find which one of the two lenses, the objective lens or the eyepiece lens, is more powerful.

To answer this question, let’s first recall that the power of a lens 𝑃 is defined as one divided by the focal length, or focal distance, of the lens, and that the focal distance, or focal length, can be found in the following way. So, for example, for the objective lens, the focal distance is the distance between the plane of the lens itself and the point at which all of the light rays from the lens are focused. In this case, we can see that all of the light rays are focused at this point here.

But importantly, the light rays on the other side of the lens must all be firstly parallel with each other, which we can see that they are. They’re all traveling in the same direction towards the right. And secondly, all of the light rays must be perpendicular to the plane of the lens, which we can see is the case. Because, for example, for the first one, we can see that there’s a 90-degree angle between the light ray and the plane of the lens itself. And the same is true for, let’s say, this ray of light. It must be because the first condition was that this ray was parallel to the first ray.

But anyway, so if the rays of light on one side of the lens are parallel to each other and moving towards the lens perpendicular to the plane of the lens, then the focal distance is the distance between the plane of the lens and the point at which all of the light rays are focused on the other side of the lens. And so, we can say that this arrow that we’ve drawn here is the focal distance, or focal length, of the objective lens. And hence, we’ll call this focal distance 𝑓 subscript 𝑜.

And we can see similarly for the eyepiece lens, the rays of light on the other side of the eyepiece lens are, firstly, parallel to each other and, secondly, moving perpendicularly to the plane of the eyepiece lens. And hence, the focal distance of the eyepiece lens is the distance between the plane of the lens and the point at which all of the light rays are focused. And we can say that that focal distance is the focal distance of the eyepiece lens 𝑓 subscript 𝑒.

Now, based on this information, we can see that 𝑓 subscript 𝑜, the focal length of the objective lens, is larger than 𝑓 subscript 𝑒, the focal length of the eyepiece lens. And if we wanted to calculate the power of each one of these lenses, then we could say that the power of the objective lens is equal to one divided by the focal length of the objective lens. And similarly, for the eyepiece lens, the power of the eyepiece lens is equal to one divided by the focal length of the eyepiece lens.

Now, at this point, we can see in our diagram, once again, that 𝑓 subscript 𝑜 is larger than 𝑓 subscript 𝑒. And hence, one divided by 𝑓 subscript 𝑜, the power of the objective lens, is going to be smaller than one divided by 𝑓 subscript 𝑒, which is the power of the eyepiece lens. This is because in the first fraction we’re dividing one by a larger number whereas in the second fraction we’re dividing it by a smaller number.

And hence, we can say that 𝑃 subscript 𝑜 is less than 𝑃 subscript 𝑒. Or another way to put it is that the power of the objective lens is less than the power of the eyepiece lens. And hence, the eyepiece lens is more powerful than the objective lens. Hence, as our answer to this first question, we can say that the eyepiece lens is more powerful than the objective lens.

Now, to look at the second question, we’re going to need to clear some space on the screen. So, having done this, we see that the second question is asking us, which of the following statements most correctly describes the effect of a simple refracting telescope on the light that passes through it? And as we saw from earlier, the simple refracting telescope consists of the objective lens and the eyepiece lens.

Now, option A says that the light rays coming from the eyepiece lens are brought to a focal point. Now, from the diagram, we can see that the light rays are traveling left to right because, for example, if we track this light ray, we see that it’s going in this direction towards the eyepiece lens and then moving this way. And so, if we’re to be talking about the light coming from the eyepiece lens, then we must be looking at the eyepiece lens from here.

Which makes sense because that’s usually where we brought our eye anyway, on that side of the eyepiece lens. However, we can see that the light rays coming from the eyepiece lens are parallel to each other, so they are not being focused at one particular point. And hence, they are not being brought to a focal point, so we can rule out option A as the answer to our question.

Moving on to option B then, this one says that the telescope makes parallel light rays from an object closer to each other. Now, looking at the first part of that statement, we can see that in this diagram, the object is emitting parallel light rays. And we can see that they are a certain distance apart from each other.

And by the end of the telescope, that is on this side of the eyepiece lens, we can see that the light rays are also parallel to each other. And that the distance between these parallel rays has been reduced compared to the distance between the original parallel rays. And so, it looks like option B might be the answer to our question. However, let’s quickly go through options C and D just to make sure that they are incorrect.

Option C says that the telescope produces an image that is larger than the imaged object. Well, from the diagram itself, we can see that that’s not true. The size of the image is smaller than the size of the object. And that is a good thing because usually with a telescope we’ll be looking at very very large objects, such as stars and galaxies. And so, If the image that the telescope produces is larger than the object itself, then this is majorly problematic. We won’t be able to see anything properly. And hence, option C is not the answer to our question.

Finally, moving on to option D, this one says that the telescope makes parallel light rays from an object further apart from each other. Well, option D is saying the opposite to what option B was saying. Option D is saying that the distance between parallel light rays at the end of the telescope, or on this side of the eyepiece lens, is larger than the distance between the parallel light rays coming from the object itself, which we’ve seen is not true. The telescope actually makes the parallel rays closer together. And hence, we can rule out option D as our answer as well. Therefore, the answer to our question is that the telescope makes parallel light rays from an object closer to each other.

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