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.
