hello and welcome to today's lesson on advanced refracting telescopes which forms part of the astrophysics option for aqa a level physics so in today's lesson we're going to look at how to draw ray diagrams for astronomical refracting telescopes so in today's lesson if we're successful and we learn we should be able to draw a ray diagram for an astronomical refracting telescope in normal adjustment to find the different types of focal length found in an astronomical refraction telescope and calculate the magnification produced by an astronomical refracting telescope so which forms the following part of the aqa a-level physics specification for the astrophysics option so there are many optical astronomical telescopes which use convergent lenses now these telescopes like mentioned are called astronomical refracting telescopes now astronomical refracting telescopes or refractors tend to be used by amateur astronomers now johannes kepler first explained the theory in some of the practical advantages of a refracting telescope constructed of two convex lens all the way back in 1611. now william gascoigne was the first who commanded a chief advantage of the form of the telescope suggested by kepler now this led to the invention of the micrometer and his application telescopic sites to precision astronomical instruments now the first powerful telescope of capillary construction was made by christian huygens after much labor and with one of these he discovered the brightest of saturn's satellites or moons titan in 1655 and in 1659 he published his system saturnian which for the first time give a true explanation of saturn's rings founded on observations made with that same instrument now an astronomical refracting telescope consists of two convergent lenses now they are called the objective lens and the eyepiece lens is named as such now the objective lens is a lens which converges the rays from the object to form a real image so this will occur as the object is more than two focal lengths away from which we've already drawn an image that this position would form in a previous lesson so it would form a real image which is what the objective lens does so the image form though is very small and difficult to observe so the eyepiece lens then magnifies this real image to form a virtual magnified image now this occurs as the object is is less than a focal length away and we've already drawn this image that this position would form an object would form from so it tells us what's going to happen now you would only ever be asked to consider an astronomical telescope in what we call normal adjustment now normal adjustment means the two lenses share the same focal plane now this doesn't mean they've got the same focal length it just means that they've been aligned so they share the same focal plane now many telescopes are kept in normal adjustment in the real world however some telescopes are actually kept out of normal adjustment but in an a level exam will only ever consider a refracting telescope where the two lenses are in normal adjustment so in this example this is the focal plane shared by both lenses because the telescope is in normal adjustment so they have the same focal plane now we can use this to define the focal lengths of the two lenses so this is how we define the focal length of an objective lens or f0 this is how we define the focal length of the eyepiece lens fe and this allows us to work out the total length of a refracting telescope because we consider it to be the sum of the two focal lengths so we can say the total length of the telescope is f o plus f e now we must be able to draw a ray diagram for an astronomical refracting telescope in normal adjustment so step one what do you do you draw a straight non axial ray that passes through the center of the objective lens and as we know before this will pass through undeflected because all rays passing through the center of a lens do not refract so this allows us to carry the ray straight on to the focal plane undetected undeflected sorry which allows us to determine the position of the image because then we draw two further non-axial rays because you tend to find that most exam questions will ask you to draw the diagram for three non-axial rays now remember they are parallel with each other because they've traveled from a great distance from another star or galaxy but they're not parallel with the actual x-axis which gives the name the non-axial rays now these rays must converge on the focal plane at the same position as that undeflected ray so it allows us to draw the image in for that particular objective lens so our image is formed on the focal plane now this is a diminished and real image now what we then do is we then draw a dotted line that passes through the point where the rays cross on the focal plane and the center of the eyepiece lens now we call this a construction line now in ray diagrams we ought we draw all construction lines as dashed lines because they are they are not showing a ray they are just allowing us they're an imaginary line to help us draw what's going to happen so a construction line is an imaginary line used to help construct images this and we denote them with dashed lines so what we then do is we continue the paths of the original non-axial ray until arrays until they encounter the center of the eyepiece lens as shown on the diagram so on ray diagrams it makes it easier to draw the eyepiece lens lower than the objective lens because of this now what then happens is we refract the non-axial rays through the eyepiece lens to leave the lens parallel to the construction line which we've previously drawn as shown in this particular diagram now the virtual image will then form at infinity which is shown by extending those lines backwards with dashed lines as shown on the diagram now our detector which in most cases will be the human eye is placed here and the detector such as the human eye will then refract the parallel lines into an image which we can observe so that is how you can form an image using astronomical telescopes in normal adjustment now you've got to be able to draw the ray diagram for this astronomical telescope now an astronomical refracting telescope will produce magnified images now a magnified image is when the image is larger than the object as shown in this particular diagram now we can measure this change with the quantity of magnification now as many objects and not straight lines it's easier to measure a quantity called angular magnification now angular magnification is the change in the angle subtended by the image compared to the angle subtended by the object as shown in these particular diagrams so this shows us the angle subtended by the image which we'll call theta i and this shows us the angle subtended by the object theta o now the point is that angular magnification is the change going from theta i to theta o sorry and or vice versa so we can say angular magnification is going to be the angle subtended by the image divided by angle subtended by the object now that gives us the angular magnification equation theta i over theta o now this equation is given to you in your examination equation book and you've got to be able to use this equation in your examination now just to be careful it doesn't matter what units you're using for angles degrees or radians as long as the units are consistent throughout the equation now angular magnification itself has no units it's just a ratio indicating a difference or a change now we can use the angle subtended by the object to determine either the diameter of the object which is the um like the planet or the star or the galaxy or the distance between the object and the actual telescope on earth so remember we're going to carry we're going to call the diameter in this instance s and the distance between the object and the telescope are now we know from mathematics which you'll cover previously that we've got an equation that s which is the diameter of the object is equal to r the distance from the object to the telescope times by the angle it produces or theta which links into the mathematical concept which you'll have seen previously s equals r theta so from this concept we assume that the angle subtended is very small so the s value becomes a straight edge or a straight line but for this to work we've got to be use radians for the angle subtended by the object now it's a very common examination question to work out the diameter of the astronomical object or the distance between the object from the angle subtended by using the equation s equals r theta now we can also use the focal lengths of the two lenses to determine the magnification of the telescope now previously we've said the focal length of the objective lens is f o and the focal length of the eyepiece lens is f e now we can work out the magnification by saying magnification equals focal length of objective lens divided by focal length of eyepiece lens or fo divided by fe now as a note we said before we consider the total length of the telescope to be the combined focal length the total length is f o plus f e as shown on this diagram now this allows us to combine the two equations to find values in question so just be aware of that because total length equals f o plus f e whilst magnification equals f o divided by f e now when we're using these particular focal lengths to turn the magnification of the telescope we need to note a couple of things that as this equation is given to us in our examination book we should be able to use this equation in your examination and it doesn't matter what the units are for lengths as long as the units are consistent throughout the equation and this magnification also has no units because it's a ratio showing change now note the magnification and angular magnification are the same value for a telescope but we only refer to a magnification as an angular magnification when it's derived from the change in angle subtended now the most effective telescopes must have a large magnification so this tells us that the eyepiece focal length which is going to be fe cannot be made too small because it needs to form a magnified image which can be observed by a human so to have the magnification as large as possible the focal length of the eyepiece lens needs to be much larger than the than the eyepiece focal length so this means that refracting telescopes need to be very long in their construction now this makes refracting telescopes difficult to construct and sag easily because they can only be supported around the edges because the radiation has to pass through the glass when it's refracting through so it makes it very difficult to construct refracting telescopes and in addition because we need such a long refracting telescope to gain such a large magnification we need large and expensive buildings to house these refracting telescopes now another issue for refracting telescopes is that they will always produce images which suffer from chromatic aberration now chromatic aberration is when an image is blurred due to the colours of varying in image position aberration means blur chromatic means color so it's a blurring of colors so these are examples of images which have chromatic aberration so you'll notice a blurring of color forms around the image as shown in here and finally shown here now the reason for this is because in this instance a celestial object such as stars in galaxies will produce visible light which is white light so white light contains lots of different wet lights of different wavelengths or colors so a lens will refract different wavelengths of color of colors by different amounts now we find the shorter the wavelength the greater the refraction so what this means is that blue light because it is a shorter wavelength light will refract a lot whilst red wavelength light which is a longer wavelength will refract less so this means blue light is refracted more than red light so this means the focal length of a lens actually varies for different wavelengths so the images of different colors form in different positions now when you're actually drawing chromatic aberration for an examination it's best to draw the rays going through either side of the lens and showing where the image is formed because this is the image drawn in your examination to explain chromatic aberration because it shows where the different images are formed for the different colours because it clearly shows that the blue light forms in a different position than the image produced from red light so all converging lenses will always produce images which will suffer from some amount of chromatic aberration now like we mentioned before large convergent lenses are also very heavy and can only be supported from the edges as otherwise the radiation will be blocked out this leads to lenses being distorted which is another issue you find when you have refracting telescopes and the final issue with refracting telescopes is that impurities and bubbles in the glass of the lens can also absorb and scatter some of the radiation so this means that refracting telescopes struggle to detect optically faint objects such as distant galaxies because on occasion the impurities and the bubbles in the glass of the lens will absorb some of the radiation so it won't be actually detected now what have we learned in today's lesson a ray diagram can be used to show the image formation in normal adjustment we can work out the angular magnification and normal adjustment with the equation of m equals theta i over theta o and the focal length of lenses can be used to derive magnification by doing magnification equals f o over f e so for being successful and we've learned in today's lesson you should be able to draw a ray diagram of an optic of an astronomical refracting telescope in normal adjustment define the different types of focal length found in astronomical refracting telescopes and calculate the magnification produced by an astronomical refracting telescope i hope you've enjoyed today's lesson on looking at how refracting telescopes work in astronomy in in astrophysics and have a lovely day