Understanding Reflecting Telescopes and Their Properties

Welcome to today's lesson looking at reflecting telescopes which is part of the astrophysics option for AQA A-level physics. So in today's lesson what we're going to do is we're going to look at how to draw ray diagrams for casagrain reflecting telescopes. So if we are successful and we learn in today's lesson we should be able to draw a ray diagram of a casagrain reflecting telescope, describe how spherical aberration can occur in a reflecting telescope And finally calculate the resolving power and collecting power produced by a Casagrand reflecting telescope, which falls into the following part of the AQA A-level physics specification 3.9.1.2 Reflecting Telescopes. So like mentioned previously, there are two main types of optical telescopes used in astronomy, refracting telescopes and reflecting telescopes. So refracting telescopes produce images when radiation refracts through glass. whilst in reflecting telescopes they produce images when radiation is reflected off glass. Refracting telescopes tend to be expensive, easily distort and are difficult to manufacture, whilst reflecting telescopes are cheaper, can be supported and manufactured a lot more easily. Refracting telescopes have an issue because they produce images with chromatic aberration, whilst reflecting telescopes have issues because they produce images with spherical aberration. Now refracting telescopes consist of two convergent lenses in normal adjustment whilst most reflecting telescopes consist of two mirrors and a convergent lens which we call a casagrain arrangement. Now you've got to be able to draw ray diagrams for reflecting telescopes in a casagrain arrangement. Now most reflecting telescopes like mentioned before have a casagrain arrangement which is a telescope consisting of two mirrors and a lens. Now the parabolic concave mirror is called the primary mirror. as it's the first mirror the radiation hits. Now this the convex mirror is called a secondary mirror as is the second mirror the radiation hits, whilst the lens in this arrangement is called an eyepiece lens as it focuses the radiation into an observable image. Now the three optical devices, the primary concave mirror, the secondary convex mirror and the eyepiece lens work together in the reflecting telescope to produce an image. Now it works with the following methodology. So the concave mirror acts as a principal mirror in the telescope. Now again, it's a concave mirror because it's shaped inwards like a cave. So if we consider axial rays, they will hit off the concave mirror and they will reflect back to a point which we'll call the focus or the principal focus as it's the primary or principal mirror. Now, this process will only occur if the mirror is perfectly parabolic. Now this is extremely difficult to do and can cause issues when making reflecting telescopes. Now if the mirror is not completely parabolic and is slightly spherical, multiple foci will form after this first reflection. So remember a focus is produced if the rays cross over each other. So only one focus is produced if the rays all intersect at the same point in space. Now this idea is called spherical aberration. with the idea of the image will be blurred if multiple foci form after this first reflection. Now reflecting telescopes suffer from spherical aberration if the primary mirror is not parabolic. So that's a very important idea to understand. Now interestingly when the Hubble Space Telescope was launched its primary concave mirror suffered from spherical aberration. So when they had the first images produced from the Hubble Space Telescope with its mirror, It actually produced images of spherical aberration, which as you can see in this particular image, is a lot fuzzier and blurred compared to an image without spherical aberration. And here's another example of an image formed which had spherical aberration. So once the Hubble began returning images that were less clear than expected, NASA took an investigation to diagnose the problem. And ultimately, the problem was traced to a miscalibrated equipment during the Mirrors manufacture. And And the result was a mirror with an aberration of 1 50th the thickness of a human hair in the grinding of the mirror. So what they did is they launched the Corrective Optics Space Telescope Axial Replacement, or COSTAR, which is about the size of a telephone booth, and placed into Hubble five pairs of corrective mirrors that counteracted the effects of the flaw. Now, once this primary mirror... has reflected the radiation to a principal focus a secondary convex mirror is placed in front of the principal mirror and what happens is as a result the image would be formed at that primary focus however they interact with the convex mirror before it does this so what happens is the secondary mirror is placed slightly ahead of the principal focus of the objective mirror. Now this arrangement is devised as if there was a detector like a human or a sensor at the point of the principal focus of the primary or objective mirror it would block out the incoming radiation. So we've got to have this Casagrain arrangement as otherwise the detector whether it be a human or a sensor would actually block out some of the incoming radiation which is what you obviously don't want. Now, the third stage is that the secondary mirror reflects the light through a hole in the concave mirror. Now, the concave mirror can have a hole in it in the shadow of the secondary mirror as no instant light can actually reach that section as the convex mirror blocks it out anyway. Now, this will form a real image beyond the primary mirror as such like this. And then step four, an eyepiece lens is then used to magnify the image in the same way as a refracting telescope. So, But just interestingly, if it's the same as a refracting telescope, it will also have the same issues. So you can actually get a slight amount of chromatic aberration in the eyepiece lens because that will also take place because refraction is taking place here. So the rays are refracted parallel from the eyepiece lens and these lines form a virtual image at infinity. Now, the primary concave mirror not being perfectly parabolic can lead to images forming with spherical aberration. So, Whilst the secondary convex mirror and its support can block out some of the incoming light and some of the reflected light will diffract around the secondary mirror. Now both of these effects will cause a decrease in image clarity. But on the good side, the large mirrors of good quality are much cheaper to build than large lenses and they can also be supported from underneath so they don't distort as much as lenses. Now all telescopes can be classified. if it's regardless of reflecting or refracting telescopes, according to two different properties. The collecting power of the telescope and the resolving power of the telescope. Now, both of these measurable quantities determine the type of images produced by telescopes. Now, these quantities both rely on the diameter of your telescope, whether it be a dish or a mirror or a lens. Now, the first property we're going to look at is collecting power. Now the collecting power is the amount of radiation which a telescope receives per second, which is why it's called collecting power. Now, the greater the area of the dish, the greater the collecting power of the dish. Now the area of the dish is directly proportional to the collecting power of the telescope. And we can assume that the dish is a circular shape, so we can say that the diameter squared of the dish is directly proportional to the collecting power of the telescope. Now a larger collecting power gives a more intense image so the telescope can observe the fainter objects in the universe. So telescopes should be built with the largest possible diameter to increase the collecting power to produce images of the faintest objects in the universe. Now the second type of property is the resolvent power. Now the resolvent power of a telescope is a measure of how much detail can be observed by a telescope. The resolvent power is the ability to see different objects as separate objects in your image. So we can commonly call this resolution. Now if a telescope has a huge magnification and a huge collecting power but a low resolvent power you will just observe a blurry image. Now the minimum angular resolution is the smallest angular separation which an instrument can distinguish between two points or objects. So if two objects have an... angular separation greater than the minimum angular separation they are seen as different objects by the telescope but if the two objects have an angular separation less than the minimum angular separation they are seen as one blurry image by the telescope. So you want your telescope to have a very low minimum angular resolution as this would allow you to see objects very close together as two separate objects. So this would allow your telescope to have a high resolution. Now the resolution of any telescope is limited by diffraction. When radiation passes through a circular aperture such as in a reflecting or refracting telescope when it literally passes into the telescope then a diffraction pattern of bright maxima and dark minima are formed. Now this pattern is formed by the constructive and destructive interference of the radiation as it passes through this aperture or gap. Now you will get the first minimum. which you can see in this particular image, which is where the first destructive interference occurs, which is shown as the first dark band around an image, and you'll also get something called an airy disc. Now this is the central maxima produced in this interference pattern. Now we can determine the minimum angular separation. of a telescope by using a theory called the Rayleigh criterion which was devised by the physicist Lord Rayleigh who also worked out why the sky appears to be blue during the day. Now the Rayleigh criterion is the observation that two light sources can be distinguished if the center of the airy disk from one source is at least as far away as the minimum, first minimum sorry, of the other source. Now you've got to learn the definition of the Rayleigh criterion terms of the Airy Disc. So in this particular image on the screen the points at the top are far apart and the points in the middle are just meeting the Rayleigh criterion where the Airy Disc is overlapping that first minimum. So they will be distinguished as two separate objects but in that bottom image the central maxima or Airy Disc of one of the objects is in fact closer to the central maxima of the other dish. the other object than the first minimum so as a result they are smaller than the Rayleigh criterion they are too close together so they are difficult to distinguish. So a telescope would observe the bottom image as one point the two objects are unresolved. Now we can express the Rayleigh criterion mathematically with an equation where the minimum angular separation which is given as theta in the equation which we give in radians approximately equal to the wavelength in meters divided by the diameter of the aperture in meters. Now to clarify this wavelength is the wavelength of the radiation. Now this equation is given to you in your equation examination book. Now you don't have to memorize this equation you only have to use it. Now when you're asked to define the Rayleigh criterion please do not give the equation as your definition rather give the Airy disk definition. Now if This equation is only an approximation as the true form of the equation is theta is equal to 1.22 lambda over d, but this is not needed for A-level physics. Now, for optical telescopes, d is the diameter of the objective lens of the objective mirror. Now, the lower the minimum angular separation, the greater the detail you can observe, so the greater the resolving power. This means a telescope with a large diameter will produce images which are highly resolved. So you have to have your telescope with the smallest minimum angular separation as possible. So a small minimum angular separation is produced by a telescope with a large diameter. Now you can't change the wavelength of the radiation received by the telescope, so as a result it's imperative you have a large diameter as possible. Now the resolvent power of your telescope is also dependent on the quality of your detector. which you've attached to your telescope. So the resolution of the detector can affect the quality of your image. There is no point having a telescope with a greater resolution than the detector, as the finer detail will be lost when registering the image with the detector. So the quality of the detector can be a large limiting factor on the resolving power, especially when it's the human eye. So just to clarify, we have two properties which we can classify telescopes with. The collecting power. where power is directly proportional to diameter squared and the resolvent power, where the minimal angular separation is approximately equal to the wavelength of radiation over the diameter of the telescope. Now, these quantities both rely on the diameter of your telescope. So you want both your quantities to have a large diameter because that will give the best properties of your telescope. So for collecting power, the larger the diameter, the greater the collecting power. the fainter the images that can be observed and with the resolvent power, the larger the diameter, the smaller the angular separation, the more the resolved the images are, which is why telescopes are built as large as possible. So to summarise what we've learnt in today's lesson, the Cassegrain arrangement is using a parabolic concave mirror and a convex secondary mirror. We can draw a ray diagram to show the paths of rays through the telescopes up to the eyepiece and we know the relative merits of reflectors and refractors. including a qualitative treatment of spherical and chromatic aberration. So if we're being successful and we've learned in today's lesson we can draw a ray diagram of a Casagrain reflecting telescope, we can describe how spherical aberration can occur in reflecting telescopes and we can calculate the resorbing power and the collecting power produced by a Casagrain reflecting telescope. I hope you've enjoyed today's lesson on reflecting telescopes and have a lovely day.

So like mentioned previously, there are two main types of optical telescopes used in astronomy, refracting telescopes and reflecting telescopes. So refracting telescopes produce images when radiation refracts through glass. whilst in reflecting telescopes they produce images when radiation is reflected off glass. Refracting telescopes tend to be expensive, easily distort and are difficult to manufacture, whilst reflecting telescopes are cheaper, can be supported and manufactured a lot more easily. Refracting telescopes have an issue because they produce images with chromatic aberration, whilst reflecting telescopes have issues because they produce images with spherical aberration.

Now refracting telescopes consist of two convergent lenses in normal adjustment whilst most reflecting telescopes consist of two mirrors and a convergent lens which we call a casagrain arrangement. Now you've got to be able to draw ray diagrams for reflecting telescopes in a casagrain arrangement. Now most reflecting telescopes like mentioned before have a casagrain arrangement which is a telescope consisting of two mirrors and a lens. Now the parabolic concave mirror is called the primary mirror. as it's the first mirror the radiation hits.

Now this the convex mirror is called a secondary mirror as is the second mirror the radiation hits, whilst the lens in this arrangement is called an eyepiece lens as it focuses the radiation into an observable image. Now the three optical devices, the primary concave mirror, the secondary convex mirror and the eyepiece lens work together in the reflecting telescope to produce an image. Now it works with the following methodology. So the concave mirror acts as a principal mirror in the telescope. Now again, it's a concave mirror because it's shaped inwards like a cave.

So if we consider axial rays, they will hit off the concave mirror and they will reflect back to a point which we'll call the focus or the principal focus as it's the primary or principal mirror. Now, this process will only occur if the mirror is perfectly parabolic. Now this is extremely difficult to do and can cause issues when making reflecting telescopes. Now if the mirror is not completely parabolic and is slightly spherical, multiple foci will form after this first reflection.

So remember a focus is produced if the rays cross over each other. So only one focus is produced if the rays all intersect at the same point in space. Now this idea is called spherical aberration. with the idea of the image will be blurred if multiple foci form after this first reflection. Now reflecting telescopes suffer from spherical aberration if the primary mirror is not parabolic.

So that's a very important idea to understand. Now interestingly when the Hubble Space Telescope was launched its primary concave mirror suffered from spherical aberration. So when they had the first images produced from the Hubble Space Telescope with its mirror, It actually produced images of spherical aberration, which as you can see in this particular image, is a lot fuzzier and blurred compared to an image without spherical aberration.

And here's another example of an image formed which had spherical aberration. So once the Hubble began returning images that were less clear than expected, NASA took an investigation to diagnose the problem. And ultimately, the problem was traced to a miscalibrated equipment during the Mirrors manufacture.

And And the result was a mirror with an aberration of 1 50th the thickness of a human hair in the grinding of the mirror. So what they did is they launched the Corrective Optics Space Telescope Axial Replacement, or COSTAR, which is about the size of a telephone booth, and placed into Hubble five pairs of corrective mirrors that counteracted the effects of the flaw. Now, once this primary mirror...

has reflected the radiation to a principal focus a secondary convex mirror is placed in front of the principal mirror and what happens is as a result the image would be formed at that primary focus however they interact with the convex mirror before it does this so what happens is the secondary mirror is placed slightly ahead of the principal focus of the objective mirror. Now this arrangement is devised as if there was a detector like a human or a sensor at the point of the principal focus of the primary or objective mirror it would block out the incoming radiation. So we've got to have this Casagrain arrangement as otherwise the detector whether it be a human or a sensor would actually block out some of the incoming radiation which is what you obviously don't want.

Now, the third stage is that the secondary mirror reflects the light through a hole in the concave mirror. Now, the concave mirror can have a hole in it in the shadow of the secondary mirror as no instant light can actually reach that section as the convex mirror blocks it out anyway. Now, this will form a real image beyond the primary mirror as such like this.

And then step four, an eyepiece lens is then used to magnify the image in the same way as a refracting telescope. So, But just interestingly, if it's the same as a refracting telescope, it will also have the same issues. So you can actually get a slight amount of chromatic aberration in the eyepiece lens because that will also take place because refraction is taking place here.

So the rays are refracted parallel from the eyepiece lens and these lines form a virtual image at infinity. Now, the primary concave mirror not being perfectly parabolic can lead to images forming with spherical aberration. So, Whilst the secondary convex mirror and its support can block out some of the incoming light and some of the reflected light will diffract around the secondary mirror. Now both of these effects will cause a decrease in image clarity.

But on the good side, the large mirrors of good quality are much cheaper to build than large lenses and they can also be supported from underneath so they don't distort as much as lenses. Now all telescopes can be classified. if it's regardless of reflecting or refracting telescopes, according to two different properties.

The collecting power of the telescope and the resolving power of the telescope. Now, both of these measurable quantities determine the type of images produced by telescopes. Now, these quantities both rely on the diameter of your telescope, whether it be a dish or a mirror or a lens. Now, the first property we're going to look at is collecting power.

Now the collecting power is the amount of radiation which a telescope receives per second, which is why it's called collecting power. Now, the greater the area of the dish, the greater the collecting power of the dish. Now the area of the dish is directly proportional to the collecting power of the telescope. And we can assume that the dish is a circular shape, so we can say that the diameter squared of the dish is directly proportional to the collecting power of the telescope. Now a larger collecting power gives a more intense image so the telescope can observe the fainter objects in the universe.

So telescopes should be built with the largest possible diameter to increase the collecting power to produce images of the faintest objects in the universe. Now the second type of property is the resolvent power. Now the resolvent power of a telescope is a measure of how much detail can be observed by a telescope.

The resolvent power is the ability to see different objects as separate objects in your image. So we can commonly call this resolution. Now if a telescope has a huge magnification and a huge collecting power but a low resolvent power you will just observe a blurry image.

Now the minimum angular resolution is the smallest angular separation which an instrument can distinguish between two points or objects. So if two objects have an... angular separation greater than the minimum angular separation they are seen as different objects by the telescope but if the two objects have an angular separation less than the minimum angular separation they are seen as one blurry image by the telescope.

So you want your telescope to have a very low minimum angular resolution as this would allow you to see objects very close together as two separate objects. So this would allow your telescope to have a high resolution. Now the resolution of any telescope is limited by diffraction.

When radiation passes through a circular aperture such as in a reflecting or refracting telescope when it literally passes into the telescope then a diffraction pattern of bright maxima and dark minima are formed. Now this pattern is formed by the constructive and destructive interference of the radiation as it passes through this aperture or gap. Now you will get the first minimum.

which you can see in this particular image, which is where the first destructive interference occurs, which is shown as the first dark band around an image, and you'll also get something called an airy disc. Now this is the central maxima produced in this interference pattern. Now we can determine the minimum angular separation. of a telescope by using a theory called the Rayleigh criterion which was devised by the physicist Lord Rayleigh who also worked out why the sky appears to be blue during the day. Now the Rayleigh criterion is the observation that two light sources can be distinguished if the center of the airy disk from one source is at least as far away as the minimum, first minimum sorry, of the other source.

Now you've got to learn the definition of the Rayleigh criterion terms of the Airy Disc. So in this particular image on the screen the points at the top are far apart and the points in the middle are just meeting the Rayleigh criterion where the Airy Disc is overlapping that first minimum. So they will be distinguished as two separate objects but in that bottom image the central maxima or Airy Disc of one of the objects is in fact closer to the central maxima of the other dish.

the other object than the first minimum so as a result they are smaller than the Rayleigh criterion they are too close together so they are difficult to distinguish. So a telescope would observe the bottom image as one point the two objects are unresolved. Now we can express the Rayleigh criterion mathematically with an equation where the minimum angular separation which is given as theta in the equation which we give in radians approximately equal to the wavelength in meters divided by the diameter of the aperture in meters.

Now to clarify this wavelength is the wavelength of the radiation. Now this equation is given to you in your equation examination book. Now you don't have to memorize this equation you only have to use it.

Now when you're asked to define the Rayleigh criterion please do not give the equation as your definition rather give the Airy disk definition. Now if This equation is only an approximation as the true form of the equation is theta is equal to 1.22 lambda over d, but this is not needed for A-level physics. Now, for optical telescopes, d is the diameter of the objective lens of the objective mirror.

Now, the lower the minimum angular separation, the greater the detail you can observe, so the greater the resolving power. This means a telescope with a large diameter will produce images which are highly resolved. So you have to have your telescope with the smallest minimum angular separation as possible.

So a small minimum angular separation is produced by a telescope with a large diameter. Now you can't change the wavelength of the radiation received by the telescope, so as a result it's imperative you have a large diameter as possible. Now the resolvent power of your telescope is also dependent on the quality of your detector. which you've attached to your telescope.

So the resolution of the detector can affect the quality of your image. There is no point having a telescope with a greater resolution than the detector, as the finer detail will be lost when registering the image with the detector. So the quality of the detector can be a large limiting factor on the resolving power, especially when it's the human eye. So just to clarify, we have two properties which we can classify telescopes with. The collecting power.

where power is directly proportional to diameter squared and the resolvent power, where the minimal angular separation is approximately equal to the wavelength of radiation over the diameter of the telescope. Now, these quantities both rely on the diameter of your telescope. So you want both your quantities to have a large diameter because that will give the best properties of your telescope. So for collecting power, the larger the diameter, the greater the collecting power.

the fainter the images that can be observed and with the resolvent power, the larger the diameter, the smaller the angular separation, the more the resolved the images are, which is why telescopes are built as large as possible. So to summarise what we've learnt in today's lesson, the Cassegrain arrangement is using a parabolic concave mirror and a convex secondary mirror. We can draw a ray diagram to show the paths of rays through the telescopes up to the eyepiece and we know the relative merits of reflectors and refractors.

including a qualitative treatment of spherical and chromatic aberration. So if we're being successful and we've learned in today's lesson we can draw a ray diagram of a Casagrain reflecting telescope, we can describe how spherical aberration can occur in reflecting telescopes and we can calculate the resorbing power and the collecting power produced by a Casagrain reflecting telescope. I hope you've enjoyed today's lesson on reflecting telescopes and have a lovely day.

Transcript for:Understanding Reflecting Telescopes and Their Properties

Transcript for:
Understanding Reflecting Telescopes and Their Properties