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Basic Physics III Lecture 18
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Title  Basic Physics III Lecture 18 
Title of Series  Basic Physics III 
Part Number  18 
Number of Parts  27 
Author 
Smy, Michael

License 
CC Attribution  ShareAlike 3.0 Unported: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal and noncommercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor and the work or content is shared also in adapted form only under the conditions of this license. 
DOI  10.5446/12954 
Publisher  University of California Irvine (UCI) 
Release Date  2013 
Language  English 
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Subject Area  Physics 
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00:05
and now I'm I'm back so I think last
00:13
week you talked about the wave aspect of life will continue in that vein and will talk about diffraction polarization eh and
00:25
this winning photo and actually shows polarization effects of flows diffraction that's pretty coast from the reflection of the glasses as soon as we these are waived like I was shown by these young double experiment there was no objection raised by the French and he said about light is really a wave then if we have some object to look at the shadow of the object in the very center of the shadow their bright spot because its equally distant from each firm With a portion of the river and therefore we should have a constructive interference at the center of if the part series correct and of course we see you almost shadow of the wave theory is correct and the center of the shadow there has to be like In clearly better predict however if 1 does the experiment carefully for circular disk like
01:35
that image after the actually don't find a bright spot in the center just like the way you could think it could use other objects for example erasable or a single slip talk so to discuss a single slip about half on energy use avoidance principal rich 1st the each portions of a Ron and considers the origin of a spherical wave then be next wave from distrust the envelope those organs so if we have a life incident on a sled each portion of the slit originates and more library and light impinging has angle with respect for the all of those Hoggins liaison phases and are pretty much goes who without a destructive interference sole heir signed fado we're favorites angle with respect to the there is a maximum meaning there's only constructive interference of all the and there's no face should however if we tell if you look at an angle with respect to the primary being viewed from that angle and there is a phase shift between horns waves we can't respond near trouble and extra and if that extra power is 1 wavelength they are the new knowledge that in the center and therefore this destructively interferes with that where the next 1 this destructively interfere with that because the same phase this 1 that and therefore there in this case signed favor equals we get destructive interference of compete so we actually get docks so if you look at mayor larger angle still let's say save Max phase should we passed on to wear the same thing happened for the bottom of till we get destructive interference those ladies at the bottom it's kind of like and making this narrow but the talks soda survivors and therefore there is some light intensity left although it's going to be fainter than the maximum equals 0 if you increase the angle further than a day to get darkness if we had tool wavelengths for the next days because again get pairwise our cancelation of individual can look at the resulting capital for a single slipped and it looks roughly like this so we have a very broad maximum center and the Max is fairly bright compared to the neighboring Max so beers Red Line Our showing intensity functional angle new CEO smaller maximum on 1 side and the same amount In between Amal changed U.S. slid list if I make this then this happened gets its why make slid wider than this happen it's now all I can change the plants which right now was approximately green and it might increase the wavelength than the pattern gets wider and decrease we now so let's look at the singles that have been the experiment you could see the
05:53
light the bright social maximum here and smaller and less intense Maxima based along and let's try to do this With a different wavelengths so the 1st lady lives lost 530 to nominate this is not 615 on the is a longer and of course this is unchanged now let's try a orderly length Of course the quantitative Paternoster saying it just spacing between and bright spot dark spots for exchanges let's try a short wavelength of the short
06:48
wavelength Julia 409 on almost half of year and just you can
06:55
see that we can serve a maximum in this case a it's essential maximum Sinaloa loss for us for red laser light to kind us 1st minimal so I
07:17
feel will could these an intensity patterns as a function of X all this speed of function declined wave number of times the diameter of the sign of the angle and we actually intensity function looks like this in case you are you're curious what you really need to know that moving a mom for this condition he can sign times across land if ever plusminus want war but not because the August the central Max and then Maxima approximately a treehouse fire crafts and so on and these single slipped minima maxima of these young doubles what happened to discussing last week so be careful when applying a formula for a single slip happened and this is the condition for only lot of Macs and unlike for the double slip experiments with maximum equally bright essential Maximum Bob Wright higher the order the maximum the rest of right it's going to be so let's
08:50
calculated example so let's assume that you have relied on wavelength 759 on leaders which passes us that this attempt minus 3 what mm wide 0 1 micron 10 to the minus 6 meters White is the central maximum in degrees How wide is it on a screen that 20 centimeters away and so that look that these conditions for minimal and read it was the 1st order minimal because we wanna Mulhall is central maximum so the 1st minimum all close former science favor equals landed divided by the diameter this is 750 not only those divided but 1 micron and that give us . 7 fire walls equals 48 . 6 degrees now that we have angle we can calculate how old followers it on the screen and to do that we are all so that the angle which is roughly 49 degrees and this is the position on the screen and the plant sending me therefore the tangent of this angle X derided by 20 2017 and that means that X 20 descending leaders times the attention of angle but these social Maxim eventually to exwife you just can't from the middle of the and therefore we get a maximum 45 . 4 cents or so let's look better said another example Soon have light shining through a rectangular hole in that Hole Maryland in the vertical direction and even in the horizontal direction as shown in the picture the question is whether you expect the diffraction pattern to be more spread out in in the vertical direction or horizontal direction based on that answer should a rectangular Spiegel the stadium Hyun narrow widened for the answer we again onlookers provision for the the minimum equals and that implies that narrow meaning that of these small gives a wider capital and therefore the year of the vertical happen this white dozens of articles slid diameter small forward speak of we want that happened to be as wide as possible so that every everybody in the stadium continued and therefore we want Of warned that is higher now also exactly the opposite the audiences this located horizontally so 1 can
11:58
apply diffraction theory to find out the limits offer resolution and various optical instruments almost any optical instrument has a circular aperture of dynamic Dean and so let's let's do another experiment and instead of illuminating a single slip that's made him whole the the ladies you see for for the pinhole is a similar happen on it now so we have a bright essential maximum twice as wide as the interference things are surrounded and this this column area after the person in areas and such area disks I actually what appears in the focal plane of imaging lends for example instead of simple docks we have assumed geometrical so and that intensity as a function of X X now Katie you'll want to ease the diameter of a circular aperture time science data and we can plot that a pattern Rollin it looks like that these central Maxim was even brighter compared with neighboring acts and in this case the intensity function in case the interests actually involves 1st vessel the 1st made therefore we don't have a sysop condition familiar mining any more of those my correct and even an lamb and the very first one is 1 . 2 2 times Thailand and so regularly delivered criterion aboard the
13:51
resolution of our optical instrument his stares actual images can distinguish if the maximum of the 2nd is at the 1st minimum of 4 so if maximal minimal and look at the picture of the
14:13
area this year we have a single image and interior Aurora will emerge are separated by lady criteria and you see you really can't I don't get any closer because you're not going to see anything shot or fielded it schematically looks roughly so we had 1 object another object here the 1st object makes diffraction pattern here the 2nd 6 1 here and people without 1 Max the 1st minimum of so we cannot this criterion to let telescopes wall microscopes redefined in the case of microscope are also trying to resolving power of R P or S which is simply angular separation from the radiator criterion multiplied the focal length and S is the shortest distance between 2 2 objects that can be resolved and assumption is this that the object is roughly located so far away from the instrument now the focal length of events can't be much smaller than its radius of curvature otherwise you won't have a Finland's and cannot see that so at the very best resolving power we get the show shortest focal length compared to the diameter and so that 1 is roughly the diameter divided too so we get the shortest as the best result how we get our roughly the wavelength 2 independent of the quality of the limiting case can't make an instrument that there's sort of 1 exception for that left with a pool and I think you were introduced last week and light go operators there's tempting To resolve where distances of 10 to the minus 15 meters using optical light and you can tho that if you good statistically high enough light intensity but it's a hit a heroic effort so Yuval instrument is limited tool we provided so
16:46
let's consider an example let's look at me Hubble Space Telescope and Hubble Space Telescope reflecting telescope that was put in orbit above the Earth's atmosphere because I had to be Bond telescopes are limited by air movements in the resolution objective diameter of novelist 2 . 4 meters and the question is for visible light for example 550 green estimated improvement in resolution earthbound telescopes if we assume that b a Walsh limits telescopes to about onehalf talks 2nd 60 arcsec Kansas 1 minute and 60 are minutes 1 big soul and in other words how 2nd the 1 with 7 thousand 400 how often oxheart monolith 7 thousand 200 degrees so we we can therefore calculated the Angolan radiance simply take 1 0 always 7 thousand 400 degrees times pie or 180 degrees which gives us 2 . what tool times 10 to the minus 6 reading and for the Hubble Space Telescope we are simply a loosely rating criteria that the resolution there EU was 1 . 2 tow times 550 not only does divided by 2 . 4 meters which Dirk gender gets 2 . 8 times 10 to the minus 7 therefore we find that found angle resolution it's 8 . 7 times larger than the hobbled in other words almost 9 times and that is in spite of the fact that earthbound telescopes usually are larger and optional objective is to add a 2nd example and this is looking at the Odyssey radio tells German Puerto Rico I recommend chicken and all it's actually quite interesting so at theaters a telescope that is 300 meters and I am so this radio a dish which is kind of like a wired network reflected on the detectors to tolerant of bother him and compare this radio telescope resolution to be 200 a telescope 1 column on mountain himself colorful for that part of our resolution 550 not only because an optical school divided by 5 . 0 8 meters objective diameter 1 . 2 2 which gives us 1 . 3 times and minus 7 ladies and steeple has a much larger objective diameter barred radio waves are much longer for the shortest wavelength measured overseas for sending to target number be good or 1 . 6 times 10 to the minus 4 read so much larger than resolution of the optical telescope however and the other advantages such a larger diameter can detect much faint objects but it's a problem for Radio Astronomy resolution this is hobbled chief general 1 that combines multiple radio telescopes largely effective dynamic another instrument was resolution is limited is a human eye and that should not just be a really criterion limits but there are multiple factors which of similar magnitude so 1st of all the resolution of the retina is best as the before we are and the call spacings on about 3 microns they'll never the diameter of the we need for the Rayleigh criterion of the pupil various from 5 . 1 centimeters 2 . 8 cents to me and if we assume green light then these really limited of resolution between 6 . 7 times 10 to the minus 4 and 8 . 4 times 10 minus directed at distances to sending leaders away from we call me of the lens and sold it where we look at s richest focal length and angular separation that gives us the EU distance on on the retinal of varied from the rating criteria and so that comes up told lie between 1 . 7 Michael meters 230 and then there's and chromatic aberrations In the and they amount to about 10 microns so we had 3 Micro meters from the operational problems we have between 2 and 13 Michael meters from the from the occurred yeah and we have about 10 imperfections the optics my soul and for from a number of weekend assumed that the sum total is roughly 20 Michael microbe that corresponds to a point for reunions and that means that we can't separate objects that I 170 meters apart distance of 20 so at a new point he can separate objects at 0 . 1 2 5 Navi look uh how well do we do with the naked eye compared to what can the best light microscope in the best light microscope would use 400 not only delight just at the edge of the and that gives us 1 halfway to wanted not only result and solar if we take the ratio of those 2 numbers come up with the rest effective magnification life my of being roughly 600 times concedes 600 times better microscope compared to make art and usually microscope use up to
23:36
1 thousand times better so reduce eyestrain that we don't have to to focus on your point acts but if you go to bigger magnification and all you going to discover diffraction with the option you want stuff that's so that at the example also I want that I could have tried my way back from Japan so if you have an airplane at an altitude of 33 thousand feet which is about 10 thousand meters and you look at the ground and assuming that model typical she was solid ground estimated the minimum separation that you need between objects so that you can distinguish them for example is it possible to Carson pop and for the and we still being spent at half milliradian angular resolution on behind a distance of 10 thousand meters multiply the tool that gives us a resolving power of about 5 meters that means that we can just Bailey con carne the large enough and just from the diffraction on all 4 released dilated pupils meaningful bright sunlight conditions baguette we can do a little bit better if you have a very good we can just barely Comcast from such of caused such a question isn't important for animals like an eagles the to distinguish small animals on the ground that now talk about it multiple and if you assemble enough of them it is called a diffraction grating so I have to stop spill let's look at he struck out to for the single slipped and now let's put slits on and there's also this slid a narrower possible so that we actually get the interference patterns of both superimposed on top of which just a complicated and still rather than make a slit the smallest possible and then we discover rediscover young experiment Melrose we can of course changed the slits separation which changes the separation of Max some are look please let and you notice that as a increased the number of slits the number of maximum become more and more prominent can't compared to the main maxim compared with a minimum of become narrower and narrower if you you have many slips basically just a bunch of bright shelf life the way we look at the a diffraction bleeding as before we look at the face different thing raised that are emitted at an angle with respect for the incident and so each neighboring Taiwan has a path length difference of Delta which is related to the space indeed times the signing of an old friend therefore we get maximum if this halflength as an integral number away from this case we can't all these signs favorite times for him equals 0 plus minus 1 plus minus 2 1 and on the reason why get such a shock but now all Macs enough for a large number of slits and he reproduce some of those scraps for example sleuths called 6 is that if we have even a slight mismatched with integral number around for example let's say just 1 thousands of away from 1 day to the next if we have 10 thousand such slips then the 5 thousand and 1st will actually be shifted by half a wave this shift multiplied if you compare this 1 . 1 5 for the 1st railroad will air destructively interfere with the 5 thousands and so on pairwise destructive interference in the already get amid even if just 1 thousands of Cleveland and therefore research diffraction gratings very precise in measuring the weekly of and can make use of that and the commenter Of course I could do a similar thing we just the prism using his diffraction gratings so the what waiters apparatus works you have a light source and that it passed through slipped and legislators located at the focal point of converging lens and therefore be generated parallel libraries or plane wave impinging on on the great and then we look at the grading the telescope and measure the angler precisely and then we get a precise measurement of correspondingly usually show was water off these of the racks of movie for convenience just 1st maxim that is not true of course if you look at everybody equals your although always get Amax independent or we not so you really want just looks at the 1st maximum and then if you have 2 different wavelengths not only 700 when they they don't appeal at the the same an angle and more than different and we can therefore separated or those with faded Close your this with polls or if we have a continuous spectrum when we see a rainbow half for the 1st 2nd and 3rd on so that those are called a spectral and that is why this instrument is coaxed the Commodores but so let's look
30:29
at an example let's determined the air angular positions of the 1st and 2nd order a maximum of 4 light of wavelength 409 leaders 709 incident on upgrading containing 10 thousand lines per so who answer that question we 1st need to find out what is the spacing between neighboring lines and so we take the 10 thousand percentage leader take universe of 1 thousand per cent there and that gives 10 to the minus 4 sending or attend minus 6 need or if you will air 1000 on so as we decide the fate of 400 not only because we now use the formula that's look at this 1 for the 700 not only the 1st order of maximum multiplied with 1 of which the M and 700 mountain leaders and divide by and the 6 needles which is facing gives us . 7 4 700 and for 400 leaders multiplied 409 abided by 10 to the minus 6 leaders that assigned fatal on on then for the 2nd order Maxima for 409 leaders there be multiplied by tool this gives us times 400 4 . 8 and 4 of 700 not only the case we get signed faded equals 124 and so we observe that signed fatal 1 . 4 is not satisfied by any angle full of these secondorder maximum doesn't exist for the 700 only case and the rest order wanted not only 24 . 6 degrees and 44 . 4 degrees for 700 wanted not only because of the 2nd order does exist and 53 . 1 it can be you there because the signing would have to be yeah 1 . 4 and so there's no angle for which assignments this is 1 . 4 so eventually you can't have infinite Bordeaux maximum because eventually use finished with your 180 degrees and let's look at another example let's look the music CD's and if it is to look at it this year because of a rainbow 1 that's typically a sign that there are some interference effects involved the question we estimated distance between the curved lines that actually contained in music which are red or the of and the 2nd part of the problem as is the same estimated the distance between the lines but in a different way now we note that the CD contains at most of 80 minutes of music and that it rotates at speeds from 200 to 500 revolutions the minute and that only the most tools of its success in a radius actually contains the lines which contains music soulful part may be simply stared that the line spacing asked me a few times wavelength of optical life which is about a point find Michael so in other words line spacing can be anywhere between point Michael needed to Michael full power being a 1st calculate the total number of revolutions and that happened in 80 minutes so take an average speed of 350 revolutions per minute and multiplied by 80 minutes than get 28 thousand revolution and that means that they have to be 28 thousand lines spread all over twothirds of 6 centimeters call for sending and the line spacing is therefore . 0 4 meters before sending divided by the number of lines of 28 thousand line that gives us a 1 . 4 Micro richest in this reasonable range the line space we got hot still the CD operates close to be diffraction when using a 650 not only delays and Saudi air it was quite important event in Japan laser diodes developed that could operate at 400 on us 1 of which so earlier today that led to the development of the Bluray device which can achieve a larger information density costly and watchful thank you very much
00:00
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