Anderson Video - Telescope

Professor Anderson
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<font color="#ffffff">So to understand the telescope we first need to go back to the single lens discussion.</font> <font color="#ffffff">Okay, and let's say that we do the following, let's say that we have a</font> <font color="#ffffff">single lens, and now let's put an object right there.</font> <font color="#ffffff">I'm gonna change colors because that pink is really squeaky today, you notice that?</font> <font color="#ffffff">All right, where's the focal length of this lens? Let's put the focal length right there.</font> <font color="#ffffff">If the object is there, where is the image?</font> <font color="#ffffff">We just did this one a second ago but let's redo it.</font> <font color="#ffffff">Parallel rays go through the focus, rays through the center don't bend.</font> <font color="#ffffff">The image clearly can't be located over here, right, these rays never meet.</font> <font color="#ffffff">But if I trace these rays back.</font> <font color="#ffffff">We did this one a second ago, it looks like the image is right there.</font> <font color="#ffffff">This is where our image is, but let's add a second lens now.</font> <font color="#ffffff">We know that a telescope has two lenses in it,</font> <font color="#ffffff">and keeping this in mind for a second, let's go back to the two lens system.</font> <font color="#ffffff">So a telescope has an objective</font> <font color="#ffffff">and an eyepiece</font> <font color="#ffffff">and we want to see a distant object.</font> <font color="#ffffff">The distant object means that the light rays coming in from it are nearly parallel,</font> <font color="#ffffff">and so it's going to form an image right in here.</font> <font color="#ffffff">And now you're going to image that image</font> <font color="#ffffff">with the eyepiece, to send it to your eyeball.</font> <font color="#ffffff">So, there is a another derivation that goes along with this problem that is a</font> <font color="#ffffff">little bit tricky but the idea is when you are looking at this image, it can in</font> <font color="#ffffff">fact look a lot bigger than it would look, if you're looking straight at the object.</font> <font color="#ffffff">And there is a magnification for the telescope, which is the following:</font> <font color="#ffffff">M is again given by theta prime over theta --</font> <font color="#ffffff">what is the angular magnification with the telescope versus without the telescope?</font> <font color="#ffffff">And in the telescope case,</font> <font color="#ffffff">it becomes this: negative fo over fe.</font> <font color="#ffffff">The negative sign just means it's upside down don't worry about that.</font> <font color="#ffffff">This is still the objective focal length,</font> <font color="#ffffff">fe is the eyepiece focal length.</font> <font color="#ffffff">So in your telescope, if you want a large magnification, then you want</font> <font color="#ffffff">the number up top to be big --</font> <font color="#ffffff">you want a long focal length objective and you want the number in the bottom to be short.</font> <font color="#ffffff">And if you think about a telescope, and you've all seen telescopes, okay,</font> <font color="#ffffff">that first lens that it hits is very far away from your</font> <font color="#ffffff">eyeball and it's not very curved, okay, it's fairly flat, that gives you a long</font> <font color="#ffffff">focal length objective. But the one at the other end of the telescope, the one</font> <font color="#ffffff">right next to your eyeball, that has a very short focal length lens.</font> <font color="#ffffff">Okay, it looks just like the eyepiece of a microscope.</font> <font color="#ffffff">So a telescope you want long objective, short eyepiece.</font> <font color="#ffffff">Microscope, you want short objective and short eyepiece,</font> <font color="#ffffff">so they're a little bit different design but it's basically the same idea.</font> <font color="#ffffff">You're trying to take small objects and make them look bigger.</font> <font color="#ffffff">The only difference is are those objects far away and you need a telescope,</font> <font color="#ffffff">if they're close, then you need a microscope.</font> <font color="#ffffff">Okay, any questions about that stuff so far? Everybody feeling okay?</font>
<font color="#ffffff">So to understand the telescope we first need to go back to the single lens discussion.</font> <font color="#ffffff">Okay, and let's say that we do the following, let's say that we have a</font> <font color="#ffffff">single lens, and now let's put an object right there.</font> <font color="#ffffff">I'm gonna change colors because that pink is really squeaky today, you notice that?</font> <font color="#ffffff">All right, where's the focal length of this lens? Let's put the focal length right there.</font> <font color="#ffffff">If the object is there, where is the image?</font> <font color="#ffffff">We just did this one a second ago but let's redo it.</font> <font color="#ffffff">Parallel rays go through the focus, rays through the center don't bend.</font> <font color="#ffffff">The image clearly can't be located over here, right, these rays never meet.</font> <font color="#ffffff">But if I trace these rays back.</font> <font color="#ffffff">We did this one a second ago, it looks like the image is right there.</font> <font color="#ffffff">This is where our image is, but let's add a second lens now.</font> <font color="#ffffff">We know that a telescope has two lenses in it,</font> <font color="#ffffff">and keeping this in mind for a second, let's go back to the two lens system.</font> <font color="#ffffff">So a telescope has an objective</font> <font color="#ffffff">and an eyepiece</font> <font color="#ffffff">and we want to see a distant object.</font> <font color="#ffffff">The distant object means that the light rays coming in from it are nearly parallel,</font> <font color="#ffffff">and so it's going to form an image right in here.</font> <font color="#ffffff">And now you're going to image that image</font> <font color="#ffffff">with the eyepiece, to send it to your eyeball.</font> <font color="#ffffff">So, there is a another derivation that goes along with this problem that is a</font> <font color="#ffffff">little bit tricky but the idea is when you are looking at this image, it can in</font> <font color="#ffffff">fact look a lot bigger than it would look, if you're looking straight at the object.</font> <font color="#ffffff">And there is a magnification for the telescope, which is the following:</font> <font color="#ffffff">M is again given by theta prime over theta --</font> <font color="#ffffff">what is the angular magnification with the telescope versus without the telescope?</font> <font color="#ffffff">And in the telescope case,</font> <font color="#ffffff">it becomes this: negative fo over fe.</font> <font color="#ffffff">The negative sign just means it's upside down don't worry about that.</font> <font color="#ffffff">This is still the objective focal length,</font> <font color="#ffffff">fe is the eyepiece focal length.</font> <font color="#ffffff">So in your telescope, if you want a large magnification, then you want</font> <font color="#ffffff">the number up top to be big --</font> <font color="#ffffff">you want a long focal length objective and you want the number in the bottom to be short.</font> <font color="#ffffff">And if you think about a telescope, and you've all seen telescopes, okay,</font> <font color="#ffffff">that first lens that it hits is very far away from your</font> <font color="#ffffff">eyeball and it's not very curved, okay, it's fairly flat, that gives you a long</font> <font color="#ffffff">focal length objective. But the one at the other end of the telescope, the one</font> <font color="#ffffff">right next to your eyeball, that has a very short focal length lens.</font> <font color="#ffffff">Okay, it looks just like the eyepiece of a microscope.</font> <font color="#ffffff">So a telescope you want long objective, short eyepiece.</font> <font color="#ffffff">Microscope, you want short objective and short eyepiece,</font> <font color="#ffffff">so they're a little bit different design but it's basically the same idea.</font> <font color="#ffffff">You're trying to take small objects and make them look bigger.</font> <font color="#ffffff">The only difference is are those objects far away and you need a telescope,</font> <font color="#ffffff">if they're close, then you need a microscope.</font> <font color="#ffffff">Okay, any questions about that stuff so far? Everybody feeling okay?</font>