Full transcript
0:02thank you but that's sort of the problem
0:07with multiple-choice tests is the fact
0:09that if you miss read something you
0:12[Music]
0:14either miss read the answers or you must
0:16read the question itself and you put the
0:18wrong one and the important thing is
0:20that when you finally know the right
0:22answer is that if you if you understand
0:28it you're good
0:29the problem is you just mean to mistake
0:31you know doing it incorrectly and that's
0:33sort of lean our problem with multiple
0:35choice tests all right so this week will
0:39be a short lesson primarily because the
0:42students in class have just spent all
0:45their brainpower
0:46on taking the test and it's been my
0:49experience in the past they don't last
0:50very long in this class after a test
0:52anyway so the other good news for those
0:56of you who are in class it's one of the
1:00rare lessons where we can not have a lab
1:03just simply because there's not really
1:04anything applicable it happens just a
1:07few times there are probably two times a
1:09semester where we don't have a lab in
1:10today's model so because the sound of
1:13happiness he writes Mita so we're going
1:16to cover a couple things I want to get
1:18through the three different types of
1:20reflection I want to get through the
1:22three cases of Snell's law and that
1:25won't give us a really good start on
1:27chapter three if you've had the
1:29opportunity to read the textbook chapter
1:31three is a rather short chapter so we
1:36want to pull out the relevant
1:37information that we have from this show
1:40you a couple formulas that we're going
1:42to be using practicing a few times then
1:44we'll be done for the day so I'm
1:46guessing we'll probably go an hour today
1:48possibly an hour beyond that I know your
1:52brains just don't have it in store next
1:53week we'll be refocused to finish out
1:55the rest of the chapter and we'll come
1:57in with fresh attitudes to tackle that
1:59material all right oh so Kim I gotta
2:02tell you the story I come in today
2:06Kendra says hey you look different
2:10did you do something to your hair
2:13and they said no and she said I find
2:16that when you tell elderly people that
2:18they're good it puts them in a great Wow
2:25Wow Wow and then she continued to talk
2:31about I don't know something that was
2:34even more offensive and indicating that
2:36I was close to 90 the 90 year olds
2:40should be happy that they have any hair
2:43at all like me and I'm like well I'm
2:46less than 90 so I think I should be
2:48happy with that I'm not quite sure so we
2:51started on a good foot there's anyone in
2:57the class want to support that I have
2:59accurately represented what she said to
3:01me and now they're all just laughing
3:04sheepishly okay so it's okay just do
3:12things that you don't mean as long as it
3:17wasn't meant then you can do whatever
3:18you want yeah okay oh I'll call that
3:20forward you mean to crash into your car
3:26but I did all right so chapter 3 let's
3:31talk about so we took sound and we
3:35described it as a longitudinal
3:37longitudinal pressure and mechanical
3:41energy that propagates through a medium
3:44we talked about the fact that pressure
3:46wave pushes particles from one place to
3:48the next we talked about how pressure
3:51waves can be attenuated or they can lose
3:54their energy as they travel a certain
3:56distance that their amplitude or
3:59strength diminishes as if propagates it
4:02turns out that that's only one
4:04interaction that sound has with matter
4:06and it turns out in in this particular
4:08chapter we're talking about the
4:09different types of interaction that
4:11pressure waves or sound waves have or
4:14interact inside of a medium so one of
4:17those and one of the most important ones
4:19we look for especially when we're
4:20talking about diagnostic ultrasound is
4:22reflection and reflection does isn't as
4:26simple as
4:26going out and bouncing off something and
4:28coming back it turns out there are many
4:29different types of reflection the first
4:32one we're going to talk about is called
4:34a specular reflection so let me go here
4:39and it might pen out so specular
4:44reflection again this is my transducer
4:48would be what happens when a sound wave
4:51travels directly down on an interface
4:56preferably ninety degrees to that
4:59interface or what we also call
5:03perpendicular or what mealy will refer
5:10to as normal incidence that's all I
5:19really do have good penmanship probably
5:22matches how good my hair looks today I'm
5:29just getting started you just gave me a
5:31mighty what normal incidence I an CID
5:36ence okay well it's supposed to say that
5:44so as we've learned from Kenter today
5:47it's not what you do it's your intent
5:50right I didn't mean it to not look like
5:52the incidence maybe so
5:59so essentially if you're 90 degrees
6:01perpendicular or what we call normal
6:03incidence to an interface especially a
6:05large smooth interface we expect that
6:08sound wave to travel out bounce off and
6:10like a mirror like reflection come
6:12directly back to our transducer that
6:17would be perfect if every single
6:19interaction in ultrasound was like that
6:22unfortunately Neely talks about the
6:25geometric aspects of sound and when we
6:29in in a normal body we have all these
6:33objects that have different angles that
6:35the sound has to move through one of the
6:40of reflection is that the angle of
6:45incidence equals the angle of reflection
6:51so how do we actually measure this how
6:55how do we actually know that this occurs
6:56let me ask you this if you had a small
6:59mirror not a full-body sized mirror but
7:02a small mirror and you wanted to see how
7:05your shoes looked on your feet you
7:08certainly wouldn't put the mirror up out
7:09of your eyes would you you would put the
7:12mirror in exactly half the distance
7:14between the height of your eyes to your
7:17shoes right half way down so you could
7:19reflect off the angle of sight visions
7:23are our light that would bounce off that
7:24mirror and then look at your shoes
7:27equally if you want to see how your hair
7:30looked if you had some you would
7:35actually look above your eyesight to see
7:38how your hair would look above your
7:40eyesight so again the angle of incidence
7:42will equal the angle of reflection so on
7:45in this the way that we actually
7:49calculate that is by drawing a
7:52fictitious line I'm going to change a
7:54color here this line that goes
7:58perpendicular to the interface which is
8:00here this is called line norm if you
8:04heard or read Miele talking about line
8:07norm
8:08it's short for normal it is a fictitious
8:13line that is drawn perpendicular to the
8:16interface itself and from this line norm
8:20can see if I choose a different color
8:22and make it very pretty
8:24what do you say no be careful now she
8:35would tell you remember I was in a nice
8:38child so so the angle of incidence is
8:41measured here from the actual beam
8:44itself to line norm we can measure the
8:47angle of incidence and equally so the
8:50angle of reflection can
8:53on the other side of line norm to the
8:56reflected beam and they should be equal
8:59so it is the oh I say for angle of
9:03incidence and it'd be Oh with the line
9:11drawn through it that's angle so the
9:13angle of incidence equals the angle of
9:15reflection and we know this is true
9:18because if you want to see your shoes
9:20you look down halfway the distance you
9:23don't look all the way to the floor to
9:24see how your she was looking to marry
9:26you look half the distance between the
9:28height of your eyes and where your shoes
9:30are right okay so this is a specular
9:35reflector and if we shoot at any large
9:39smooth interface and preferably if we
9:43shoot perpendicular or what we call
9:45normal incidence we should get a lot of
9:47reflection from that interface as long
9:50as one other characteristic is true and
9:53that is if impedance one is is not equal
10:00to the impedance of the medium medium
10:02two meaning there must be an impedance
10:08mismatch between the first medium and
10:11the second medium otherwise the
10:13interface will not be reflected you
10:21would think so far yeah as long as the
10:25impedance of medium one which would be
10:27perhaps everything in here does not
10:31equal the impedance of medium two which
10:34is everything down here long as there's
10:37some big mismatch there will be a
10:38reflection at their interface okay so
10:47impedance is made up of a couple things
10:50the tissue density which is we discussed
10:54already density is actually one of the
10:56things that determine the speed of sound
11:02because of density increases of course
11:05the velocity
11:06decreases it's one of the
11:08characteristics of a medium and how well
11:11something propagates and that multiplied
11:14by the velocity of the meeting which as
11:18we also said was made up of a lot of
11:20things not only including density but
11:22including bulk modulus elasticity and
11:27compressibility so all those
11:29characteristics go into calculating a
11:31particular impedance of a medium and
11:34there will be a reflection of two
11:36different mediums having different
11:38impedances are next to each other as
11:40that sound goes through it there will be
11:42some form of reflection all right so
11:46this is one formula that we're going to
11:48look at and I just want to walk you
11:51through one of these so we know that a
11:54common velocity that we deal with this
11:58fifteen forty meters per second so if
12:00that's the velocity and I gave you a
12:02density of 1,000 kilograms per meter
12:08cubed please take a minute and calculate
12:11the impedance of this particular medium
12:15so you would set it up Keeton's equals
12:19one five four zero meters per second
12:23multiplied by 1,000 right so I'll show
12:30you the way that you could do it if you
12:31don't trust me that that's just going to
12:32be three decimal places more so if we
12:34want to go back to one we can go ahead
12:36and subtract three zeroes and turn that
12:39into a 1 whatever we subtract we're
12:42gonna have to add so it would be 1
12:45million five hundred and forty thousand
12:49meters per second multiplied by one what
12:52was a telegram from meter cubed right so
12:57we know like we said the math wasn't the
12:59hard part my 1 million five hundred
13:00forty thousand but now we're left with
13:03this mess of multiplying meters per
13:06second multiplied by the units of
13:09kilograms over meters cubed right so
13:14because we have one meter in the
13:16denominator here and three of them in
13:19the dependent
13:20they say that backwards one meter in the
13:24numerator and 3 in the denominator we're
13:27going to take that away and turn this
13:29into a two so we end up with kilogram
13:33still on top and then we end up with
13:37meter squared and seconds on the bottom
13:42kilograms per meter squared seconds is
13:47the same thing as a real which is a way
13:51that we measure impedance and it turns
13:55out that since we know that velocity
13:57typically is in the 1500 range for
14:02ultrasound we also know that the density
14:05of soft tissue is somewhere around a
14:09thousand kilograms per meter cubed it
14:12turns out a lot of our impedances for
14:17soft tissue structures are in the
14:20millions of rails and we oftentimes just
14:25call them mega rails so this would be
14:28one point five four mega rails so let's
14:35try this one more time so we feel nice
14:39and good about it
14:41so again if an e this is equal to
14:46density times velocity let's say the
14:48velocity in this case is 2,000 meters
14:52per second and the density is 1,000
14:58kilograms per meter cubed what is the
15:03impedance in mega rails
15:18all right what answers did you get so I
15:21got 20,000 kilograms over 20,000 and
15:29anything anybody have anything else
15:31other than 20,000 2 million okay so here
15:42we go again
15:43beaten sequels density 1000 kilograms
15:49per meter cubed multiplied by 2,000
15:54meters per second
15:56we know that the units are going to come
15:58out in rails right so all we have to do
16:02is figure out what 1,000 times 2,000 is
16:09and again you can go ahead and take away
16:12three decimal places here and whatever
16:13we take away we need to add over here so
16:161 times 2 million is 2 million rails or
16:23and we wanted it in mega rails so two
16:27million rails is the same as two rails
16:31right very good with that
16:37all right good now let's go back to this
16:42specular reflection because we said
16:44there must be an impedance mismatch in
16:47order for some form of reflection to
16:49occur specular reflection is defined by
16:52this one normal incidence or
16:54perpendicular to an object to a large
16:58smooth interface and three an impedance
17:01mismatch will find that an impedance
17:03mismatch must be present for all forms
17:06of reflection but those three
17:09characteristics must be there in order
17:11to define that we have a specular
17:13reflection specular reflections are very
17:17bright large objects on our ultrasound
17:21screen so let's look at that for just a
17:24second
17:27[Music]
17:29so here's a large smooth interface that
17:37those would be specular reflection
17:39reflectors that's different from all the
17:42dots that make up the rest of the image
17:44here and here but we do have a large
17:48smooth reflective object there that
17:51would be a specular reflector
17:52these are specular reflectors here here
17:55here here here here
17:59back here those are all specular
18:02reflectors everything else is what we
18:04call diffuse reflection or scattering
18:06then make up this image so there are
18:09plenty of examples there's also this one
18:14see the back of the baby's head here as
18:17a large specular reflector and these
18:20combined together creating the vertebrae
18:24of the spine and the baby's neck and
18:26here as well these are all all
18:30considered specular reflectors by
18:32ultrasound again in order for that to
18:34happen you must one have an impedance
18:36mismatch so it so it can bounce off of
18:39something if there's no impedance
18:40mismatch you don't see this interface -
18:43it should be roughly 90 degrees or close
18:47to it three there the object must be
18:52large and smooth so those are the
18:56requirements for specular reflection
18:59which say what one more time three
19:04things normal incidence or near normal
19:08incidence or perpendicular to the object
19:13to an impedance mismatch
19:24okay three large smooth interface normal
19:32incidents are perpendicular that's okay
19:39we got it was specular reflector all
19:43right so moving down here the next type
19:47of reflection I'm going to skip all this
19:51part up here really there it is it's at
19:57the bottom of specular reflections
19:59called diffuse reflection so diffuse
20:02reflection is slightly different than
20:05specular reflection and that diffuse
20:07reflection if we have our transducer and
20:11we're going to send a sound beam down
20:13instead of having a large smooth
20:16interface that work perpendicular to we
20:19have any regular object and we're going
20:24to interact with remember we said the
20:27angle of incidence always equals the
20:28angle of reflection when we're talking
20:31about reflection so if we shoot down
20:35here and we happen to hit this at a
20:37slightly different angle it'll bounce
20:40off for the slightly different angle and
20:42if we were to move the transducer over
20:45here we've come down here and then the
20:48angle of incidence would equal the angle
20:50of reflection here and if the beam hit
20:52over here it would bounce off over here
20:55and if it hit
20:57I don't know down here it bounced off
20:59over there so from this irregular or
21:03diffusely irregular object would be you
21:06would have multiple angles of reflection
21:08heading back that would not go directly
21:10back to the transducer we call this
21:13diffuse reflection also known as
21:24scattering
21:35so the following conditions must be
21:37there for diffuse or diffused reflection
21:40or scattering one large object or
21:45specifically a large non smooth object -
21:53as always for any type of reflection
21:56there must be an impedance mismatch
22:08so any large contributor surface object
22:13that has an impedance mismatch between
22:15the medium and the object itself will
22:18create diffuse reflection or scattering
22:27so going back to what the scattering
22:30look like this is what scattering mostly
22:38looks like so it is what makes up all
22:41the tiny little dots inside of an object
22:45all of that there is scattering all of
22:51this inside of this object is scattering
22:55um these large smoother ones are
22:58specular x' including the striations of
23:02the tissue itself but all of these dots
23:06inside of here are all made up by
23:08diffuse reflection and scattering egg
23:13now the last type of reflection is known
23:20as Rayleigh scattering and I can't show
23:26you what it looks like because you will
23:29never know if it's happening or not but
23:31it could by theory happen what Rayleigh
23:34scattering is is and this is different
23:37from the other two types of reflection
23:38we talked about the other two are large
23:41objects one being very smooth for
23:44specular reflection and one having an
23:46irregular surface for diffuse reflection
23:48in Rayleigh scattering the objects are
23:52tiny one time do you have no you don't
24:08see Rayleigh scattering like the size of
24:12a blood cell so what typically happens
24:17is they have impedance mismatches
24:20between
24:21the serum around them or the objects
24:24behind them so technically they can
24:26cause reflections however the beam
24:29itself is oftentimes so small or
24:33bypasses around these objects they're
24:36not big enough to reflect the entire
24:38beam so instead the beam sort of bounces
24:41off it and goes up in different
24:43direction it may go right through it
24:44completely it may create a reflection
24:47but you'd never see it because it
24:49doesn't carry the amplitude large enough
24:51to be seen so a lot of times we don't
24:54even found often but technically they
24:57could create reflections but we would
25:00never see them because they don't create
25:01enough of a reflection for us to see
25:03them so this is called Rayleigh
25:07scattering and often times they would go
25:11off in such directions that we'd never
25:14know if or when they'd ever get them
25:19back all right so I think Neely let's
25:26see as a great animation somewhere oh
25:34yes there's me Lee's so you have all
25:38these lines of sight heading down here
25:41it looks here this one that went all the
25:46way through the collection of cells this
25:49one here went here and then bounced off
25:51and head off in that direction this one
25:55came here and hit the side of this one a
25:56bit in a different direction
25:58so yeah you either hit or miss we're not
26:01seeing at all because they are so small
26:03so that's called Rayleigh scattering and
26:06again you may never see these echoes
26:09anywhere but because they have impedance
26:11mismatches some reflection occurs all
26:14right so the amount of reflection that
26:20occurs at any particular interface is
26:22dependent on its intensity reflection
26:25coefficient so this the intensity
26:32reflection coefficient
26:35and be calculated by comparing the
26:38impedance of medium to to the impedance
26:42of medium one dividing it by their
26:45differences as well
26:50in taking that whole value and squaring
26:53it now this looks a lot worse than it
26:56really is but as we discovered earlier
27:00that most of our impedances in
27:04soft-tissue are typically in the mega
27:07rails right so if I had the impedance of
27:13medium one and let's say that was one
27:16mega rail and the impedance of medium
27:20two and that was two mega rails could we
27:24calculate how much reflection occurs at
27:27that particular interface and using this
27:30particular formula the answer would be
27:33yes so we would just plug it in so we
27:35would say in this case the impedance of
27:38medium 2 is 2 the impedance of medium 1
27:42is 1 divided by the impedance of medium
27:452 plus the impedance of meeting 1 in
27:48that whole value squared right
27:52so 2 minus 1 is 1 right 2 plus 1 is 3
27:59that whole value squared
28:03what's 1/3 squared one ninth right so 1
28:09divided by 9 and then we divide that 9
28:12into one doesn't go into 1 but it will
28:16go into 10 one time 9 with 1 left over
28:20and again we'll repeat this again but
28:23the answer to this particular problem is
28:26the coefficient of reflection is equal
28:29to point 1 1 now you're saying what in
28:32the world does that mean the coefficient
28:37of reflection describes the fraction of
28:39energy that is reflected at that
28:42interface based on these two impedance
28:45these two impedances of medium one and
28:47medium
28:48- so if I calculated a coefficient of
28:55reflection of 0.1 one the best way to
28:58put this into something that most people
29:01understand is turn it into a percentage
29:04do you remember doing this I think day
29:06one in this class how do you turn a
29:10decimal into a percentage multiplied by
29:15a hundred and what would the answer to
29:16us be so the percent reflection is
29:21actually equal to 11 percent so does
29:24that make more sense based on those two
29:27impedance differences we now plug it
29:29into a formula in a tolis the fraction
29:32of energy that was reflected in that
29:34particular interface or the percentage
29:37can be calculated calculated by simply
29:39multiplying by a hundred or eleven
29:42percent of its energy is reflected at an
29:45interface where the impedance of medium
29:472 is 2 mega rails and the impedance of
29:49medium one is 1 mega rail so that makes
29:51sense to you okay so the reason why I'm
29:54making you go through this exercise at
29:56least mentally is that melee has I'll
29:59show you because I wrote them all down
30:02that was fascinated by how many of them
30:04there were it's not that one it's this
30:07one
30:08all of these these calculate the
30:11coefficient reflection the coefficient
30:13of transmission the percent transmission
30:15and the coefficient of trip and the
30:17percent reflection these are actually
30:20four different formulas to remember what
30:24would be considered I think common sense
30:26because you've already told me you can
30:29calculate the percent reflection from
30:30the coefficient of reflection right just
30:33multiply by 100 you don't need a
30:34separate formula to do that so going
30:38back to this if the coefficient of
30:42reflection was 11% what that means is I
30:44had a hundred percent energy hitting a
30:47particular interface and if a hundred of
30:50a hundred percent at the first interface
30:5211 percent of it was reflected back
30:55how much is remaining
31:00maybe nine so what you're saying is the
31:03percent transmission is 89% did we need
31:08another formula the one that said four
31:10times the impedance of medium 2
31:13multiplied by the impedance of medium 1
31:15divided by impedance medium 2 you get my
31:18point right I didn't need another
31:20formula to calculate that I used common
31:22sense right so from the coefficient
31:25reflection we have already calculated
31:27not only the coefficient function the
31:29percent reflection and the percent
31:31transmission there's only one left
31:33it's a coefficient of transmission so if
31:37the percent transmission is 89% what do
31:39you think the coefficient of
31:40transmission will be in a decimal B no
31:46you just calculated the coefficient
31:49reflection coefficient of transmission
31:51percent reflection and percentage
31:53transmission by using one form not full
31:59so that formula again is the coefficient
32:02reflection equals being eaten some
32:06medium to minus the impedance of medium
32:08one divided by the impedance of medium 2
32:11plus convenes a medium one that value
32:15squared from the coefficient reflection
32:17you can calculate the other three the
32:21other coefficient or transmission as
32:23well as the percentages of reflection
32:24and transmission using common sense
32:27right yes yep so the percentage
32:36transmission would be because we start
32:38with a hundred percent and if we lose a
32:40lot of percent got it okay so what I'd
32:44like to do is just run through this
32:46fairly quickly I'd like you to tell me
32:49the coefficient reflection the
32:51coefficient of transmission the percent
32:53transmission and the COPE sorry take
32:57that back and the percent reflection if
33:04the impedance a medium one let's say is
33:091 mega rail
33:12that's too many bill and the impedance
33:18of medium to is let's say three mega
33:21rails okay give you some time to work
33:25through I need those three answers let's
33:28see how we do
33:32so for coefficient and reflection we got
33:40answers wait you don't know which one
33:45goes to which way did you calculate and
33:51then I did this three plus the one and
33:54then we give you the 1 over 4 and then
33:55you'll square root is the 1 over 16
34:00correct
34:00we whoa so it's 3 minus 1 first right on
34:07the top right ok so let's go through
34:12this so it's 3 minus 1 and then 3 plus 1
34:19right right so 2 over 4 and that whole
34:30value squared right so 2 squared is 1/4
34:37squared is a lot right so then we just
34:42go I mean we can simplify this if you
34:44want go down to 1/4 right and then that
34:49would be equal to 0.25 everybody agree
34:52with that right I'm running out of room
34:54so let me how did you do it differently
35:06yes and so if you went 16 divided into 4
35:13oh my goodness is 1 take awhile but 16
35:17would go into 40 right and 16 would go
35:21in there oh my goodness I'm gonna run
35:23out of room
35:24we take it to the next page to show you
35:27so 16 into 4 16 when going to 40 twice
35:3436 and 4 left over and you drop down by
35:41step
35:41that's interesting point 2 - ya know why
35:48it doesn't come on right I didn't I am
35:5232 am i doing my man oh oh that's why
35:55you're right sorry
35:57it is 32 this would be 8 right so 16
36:01would then go into 8 5 times so there's
36:04the 0.25 we were looking for so the
36:06coefficient of reflection remember this
36:08is the fraction of energy that is
36:10reflected at that interface is 0.25 if
36:13the coefficient reflection is point 2 5
36:15what is our percent reflection
36:20it's that 4 multiplied by 100 right 5
36:25percent if we lost 25% and we started
36:30with a hundred percent what is our
36:31percent transmission what's going on 75
36:35percent and if that is the percentage of
36:38transmission what is the coefficient or
36:40fraction of that percentage there we go
36:47to the other one what sounds like you
36:59[Music]
37:01yeah yes we got those pretty good okay
37:07so now we can calculate the amount of
37:10reflection and the amount transmission
37:12at any given interface if we know that
37:15there are two as long as we know if
37:19their impedances are mismatched the next
37:22exercise I want you to do is this one
37:25also calculate the amount of reflection
37:30the coefficient of transmission the
37:33percent transmission and the percent
37:37chené yeah if the impedance of medium
37:39one is 1 mega rail and the impedance of
37:45medium 2 is 1 mega rail try that one yes
37:53so if there's no impedance mismatch
37:56reflection does not occur right so for
38:03specular reflection there must be an
38:05impedance mismatch also a large smooth
38:07interface and hopefully an angle that is
38:10close to perpendicular in normal
38:11incidence for diffuse reflection also
38:14known as scattering it's a large
38:16irregular surface but there also must be
38:19an impedance mismatch and lastly or
38:22Rayleigh scattering
38:23there must be an impedance mismatch but
38:26again this is extremely small surfaces
38:29and oftentimes we don't see these
38:31reflections at all so everybody
38:33comfortable with the three types of
38:34reflection we've discussed so far how to
38:38calculate impedance and how to calculate
38:42the coefficient reflection the
38:44coefficient of transmission percent
38:46transmission and the percent reflection
38:49of any given interface yeah all right so
38:55now go back to all of this refraction so
39:08refraction whereas reflection is simply
39:10bouncing off an object and having it
39:12bounced in a different direction or
39:14directly back to the source itself
39:16refraction is the bending of sound like
39:19the bending of light if you've ever
39:21looked at someone standing in a pool and
39:24it looks like their feet or their legs
39:26are really short
39:27that's a refraction of light okay you
39:30don't notice that when the person steps
39:32out of the pool because there's nothing
39:34bending the light to make your eyes see
39:37things differently and it turns out if
39:39the pool is really wavy it almost looks
39:41like their feet are dancing underneath
39:44the water because it's constantly
39:46bending the light in different direction
39:47and your vision is bouncing off of
39:51angles that see things differently than
39:53they are in reality it also happens with
39:56sound it turns out sound can be bent as
39:58well so melee has some really good
40:02animations to show how this happens but
40:04I'm going to try to recreate it on here
40:07so how this actually happens is that we
40:11take see how an interface like this and
40:19let's say eCos sound travels and
40:22wavefronts we're gonna create a wave of
40:24energy heading towards this particular
40:27interface and let's say the medium up
40:30here is slow and the speed of this
40:34medium is fast so the because of the
40:39concept of heightens principles and says
40:41that Huygens principles in order to push
40:44particles can you hear me we have is a
40:46collection of tiny little wave fronts
40:48all creating and pushing particles in a
40:53certain direction so as is this
40:55wavefront think of it as like a water
41:00wave as it hits the short what nice I
41:25don't think your screen at all I don't
41:28see any writing I just see a white white
41:30board what here yeah I see your action
41:37you know I think nothing you see nothing
41:39nothing this your white board if you
41:42weren't worried hey what do you see now
41:44I now it looks like it might work okay
41:48so do you see this yes okay all right so
41:52let's start again so we have an
41:54interface let's make it a little more
42:03all right so again the medium up here is
42:07slow this is fast like I was saying the
42:10Huygens principle says sound travels in
42:14wave fronts if you all kind of string
42:16together so imagine a bunch of people
42:18arm-in-arm walking us one particular
42:22line towards I don't know a line or
42:27something like that and what's going to
42:29happen as these people reach this line
42:33the ones that cross over first are going
42:36to begin walking much faster Hey while
42:41the other ones behind still walk at the
42:42same speed and these keep moving faster
42:45in this direction while these guys
42:49continue to move slow and they keep
42:52moving farther ahead to where they're
42:54almost ahead and by the time they get
42:56all the way across what has happened is
42:58we have bent the trajectory of this line
43:01or people moving in this direction and
43:04this is what happens with a change in
43:08speed because wave fronts cross an
43:11interface at different times then the
43:16part of the way that crosses first is
43:18going to take on the speed of that
43:21second medium quicker than the the rest
43:24of the wave front that is still stuck in
43:26the old in the old medium so for this
43:32reason can you see this I see your your
43:43Z equals PC model now it's blank yep but
43:48it look like it's gonna work okay so the
43:52first interaction of Snell's law is
43:57simply what we just described and that
43:59if we have the impedance of medium to is
44:04faster than the sound wave travels here
44:08and what we anticipate is going to
44:10happen from line norm is that that
44:15particular
44:17wave should continue in a straight line
44:20however if the velocity and medium 2 is
44:23greater than medium 1 it's going to bend
44:27away from line norm just like what we've
44:29just described it's actually whistle
44:33it's not new around this to black it's
44:35actually going to bend off in this
44:36direction because it's moving faster
44:42than the first medium so if the
44:45impedance medium 2 is greater than
44:50medium 1 the transmitted beam will Bend
44:57away from Lai norm and create a greater
45:01angle of transmission if the impedance
45:11the medium 2 is greater than the medium
45:131 the transmitted beam will Bend away
45:19from line form and create a greater
45:23angle of transmission what medium 2 is
45:34greater than medium 1 ok the transmitted
45:46beam okay will Bend away from line norm
46:06okay or create a greater angle of
46:12transmission
46:26it's yes everything is the opposite
46:29though pinking it back oh I didn't mean
46:34to like erase the whole thing but yeah
46:39the impedance and medium 2 is less than
46:43medium 1 our line norm here here's our
46:57line coming in and what I'll actually do
47:00is bend towards line norm from its
47:05anticipated path so if the impedance of
47:12medium 2 is less than medium 1 it'll
47:15bend towards line norm or create a less
47:18angle of transmission and even write it
47:23in this little hole what stop good does
47:52anybody have my notes is it in my notes
48:04I'll make sure plus if you read it down
48:12you learning that's alright Emily you
48:18good it's true yeah ok so let's talk
48:23about case three Snell's law so that
48:26describes case one and case two case
48:27three just
48:29I have something that's kind of
48:30different so with case three this is a
48:34person I want to draw line norm again so
48:37you know where we're at so case three
48:41says something unusual kind of happens
48:44if the angle of incidence exceeds the
48:48critical angle so what is the critical
48:51angle and it turns out the critical
48:53angle is not an exact angle it's more
48:58related to the amount of difference
49:00between medium of 1 and medium 2 so in
49:05case 3 if the angle of incidence passes
49:09the critical angles and we have a rather
49:12steep angle of incidence on this media
49:16and if the impedance of medium 2 is
49:20greater than medium 1 like a stone
49:25skipping on water it'll never enter
49:29medium 2 and it literally will skip
49:31across the surface of that interface I
49:40think I just did it please be a means of
49:43medium to it's greater than medium 1
49:56and the angle of incidence exceeds the
49:59critical angle I'm just repeating what's
50:18in my note and they ain't all of
50:20internets exceeds the critical angle
50:29it's not always I'm gonna get to that
50:32critical angle thing Savita it's not
50:34always 22 degrees however most authors
50:37agree that at 22 degrees total internal
50:43reflection which is also known as case
50:45three Snell's law happens regularly if
50:51that helps
50:53so episode so in this particular case
50:57the critical angle is dependent on the
51:01amount of difference between the medium
51:031 and medium 2 in terms of their
51:05impedances most authors agree that the
51:09critical angle hovers around 22 degrees
51:11angle of incidence and it may fluctuate
51:15slightly depending on the amount or
51:20magnitude of difference between their
51:21impedances so roughly at 22 degrees or
51:25greater you can reasonably believe that
51:28case 3 Snell's law also known as total
51:31internal reflection will happen
51:32regularly not a guarantee but pretty
51:37regularly what well that's an angle of
51:45incidence so in this case nothing is
51:58transmitted into medium 2 which is why
52:02they call it total internal reflection
52:09so beat it as a help yes what I wish I
52:22could be very black and white but
52:24unfortunately most would agree that a 22
52:28degrees or angle that yes total internal
52:30reflection will happen unfortunately
52:32it's not an absolute it's a it's a
52:36probably will happen it just depends on
52:39how fast medium to actually is alright
52:43so we understand the three different
52:45types of refraction one of the medium
52:49and medium to is too fast and it bends
52:52away from my norm to the medium is
52:56slower independence back towards lying
52:58norm creating a less angle of
53:00transmission and lastly case three
53:03Snell's law so known as total internal
53:05reflection give the velocity medium to
53:07is greater and the angle of incidence
53:10exceeds the critical angle it'll skip
53:14across the surface be good with those
53:17three different types of refraction okay
53:20and lastly one more thing about this is
53:23discovered this is governed by a formula
53:28or concept known as Snell's law this
53:33describes refraction and it says there's
53:36a relationship between the velocity and
53:38the incident medium to the velocity and
53:40the transmission medium related to the
53:43angle in the incident medium and the
53:47sine of the angle and the transmitted
53:51medium now the beautiful thing about
53:53this particular formula is that you'll
53:55never have to work it because it has
53:56signs in it
53:57and since calculators are allowed on
54:00your board you simply have to recognize
54:02and go oh this is making a relationship
54:04between velocity differences and angles
54:07between those two mediums that is known
54:11as Snell's law which describes the
54:14internet interaction known as refraction
54:17good
54:21to the CI oversee to speed over safety
54:25what is one tonight that's what it says
54:44sine of angle insolence divided by
54:47saying that the sine of the angle
54:49transmission all right any questions
55:07about refraction or reflection which are
55:14the only two interactions that we've
55:15discussed so far in Chapter three there
55:25were three there were two large
55:27irregular surface and meant impedance
55:30mismatch any other questions
55:34whoa it just put that out that's for my
55:38trivia in in class in my class though so
55:43this is your question no it's not my
55:46question is it correct to say that all
55:51sound waves will reflect but not all
55:53refract only sound okay yes it's true
56:07that yeah what why am I in screen
56:17because I think it's a question right
56:24are you an are you asking this question
56:27to your students camera system from your
56:30students who would like me to address
56:32yeah
56:33you addressed Tricia asked it in my
56:35class I mean I answered it but you know
56:38like let her hear it from you or just
56:39kiss my right making one one concept in
56:43this that I did not make very clear is
56:46that I mean I always drew it that way
56:48but yes
56:49refraction requires an angle other than
56:52normal incidence that is no refraction
56:54will occur if you're normally incident
56:57or perpendicular to an interface
56:59I don't think it is a correct statement
57:01that say that all sound waves will
57:04reflect as we figured out today in class
57:07that 15 penis mismatch is identical no
57:10reflection will occur so so yes I agree
57:14that no refraction will occur at normal
57:16incidence they don't agree that all
57:17sound waves will reflect said you think
57:21answers are addressing that question I
57:23think you're good okay all right any
57:26other questions we'll finish chapter
57:57three next week thanks thanks recording
58:02off