Basic Physic III Lecture 16
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Basic Physics III16 / 27
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Particle physicsMultimeterMagnetic resonance imagingKüchenmaschineCompound engineMicroscopeFlight information regionTelescopic sightMixing (process engineering)Optischer HalbleiterverstärkerPower (physics)Speckle imagingCamera lensNegationElektronenkonfigurationCosmic distance ladderSubwooferNanotechnologySizingNear field communicationPlane (tool)DayStarFocus (optics)Curved mirrorSpare partIntensity (physics)Noise figureMicrophoneMicroscopeRear-view mirrorCompound engineOrder and disorder (physics)Cartridge (firearms)Schwache LokalisationJet (brand)Diving suitFACTS (newspaper)Augustus, Count Palatine of SulzbachMinuteHose couplingMotorcycleGebr. Frank KGFocal lengthFinger protocolAxleEnergy levelYearElektronenbeugungRoll formingOrbital periodLecture/ConferenceComputer animation
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CaliberCompound engineScanning acoustic microscopeMixing (process engineering)KüchenmaschineSmart meterJuneMicroscopeOptischer HalbleiterverstärkerCamera lensMagnetFormation flyingRelative articulationDistortionCosmic distance ladderFocus (optics)Interference (wave propagation)ProtectionStandard cellCamera lensWeightMinerHourSingingWind waveFocal lengthFACTS (newspaper)Car dealershipPhotographySpare partBill of materialsTuesdayLagenholzTwilightProzessleittechnikRefractive indexColorfulnessSpeckle imagingRainNoise figureMitsubishi A6M ZeroChromatic aberrationFisheye lensWhiteSubwooferOptical aberrationNear field communicationLightOrder and disorder (physics)ForgingCasting defectWavelengthComputer animation
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Wind waveDiffractionLightInterference (wave propagation)WeightParticleMinuteLecture/Conference
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MechanicWind waveInterference (wave propagation)AmplitudeLecture/Conference
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Wind waveJuneInterference (wave propagation)Lecture/Conference
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MechanicWhiteWind waveWavelengthMitsubishi A6M ZeroCartridge (firearms)Interference (wave propagation)WeaponEngine displacementCardboard (paper product)Brillouin zoneDrehmasseLecture/Conference
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Phase (matter)Interference (wave propagation)LightOrder and disorder (physics)Source (album)WavelengthWafer (electronics)Standard cellWind farmTurningYearWeightMondayCoherence (signal processing)Lecture/Conference
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Interference (wave propagation)LightWavelengthWind waveCosmic distance ladderScreen printingSource (album)Single (music)Bubble chamberPitch (music)WeightPlatingSpring (season)Lecture/Conference
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Relative articulationWinterInterference (wave propagation)Moving walkwayLightCosmic distance ladderPattern (sewing)Lecture/Conference
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LightSource (album)Cosmic distance ladderInterference (wave propagation)Wind waveBrightnessMoving walkwayLecture/Conference
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Lecture/Conference
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WeightSource (album)Cosmic distance ladderWavelengthWind waveLecture/Conference
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Interference (wave propagation)Wind waveLightBrightnessCosmic distance ladderScreen printingWavelengthDiffractionSingle (music)GruppensteuerungCartridge (firearms)Coherence (signal processing)Source (album)LaserSizingQuality (business)Order and disorder (physics)Pattern (sewing)MeasurementToolNoise figureLecture/Conference
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Cosmic distance ladderSensorLecture/Conference
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Interference (wave propagation)WavelengthCosmic distance ladderScreen printingMultiplizitätWind waveOrder and disorder (physics)Source (album)RiggingModel buildingDuty cycleAccess networkCamera lensCar seatWeightCylinder (geometry)Lecture/Conference
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Bending (metalworking)MultiplizitätInterference (wave propagation)Finger protocolBrightnessLecture/Conference
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WavelengthGlitchLecture/Conference
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Interference (wave propagation)SpaceportFinger protocolLumberLecture/Conference
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Interference (wave propagation)Screen printingCartridge (firearms)Cell (biology)PlatingLecture/Conference
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Screen printingVideoDirect currentPlumb-bobDiving suitCosmic distance ladderEquinoxField-effect transistorRoll formingSpare partSingle (music)Angle of attackAlcohol proofLecture/Conference
Transcript: English(auto-generated)
00:04
All right, so let's just wrap up our discussion of a telescope. So practically speaking, if the object is from very far away, the intensity would be very, very faint, right?
00:21
So the way to compensate the intensity is that we need a large diameter for the objective length. And this is practically done through these two lens configurations.
00:40
So instead of having lenses, we make use of the mirror instead, all right? So here are the parallel rays that come from distant objects like stars and they get reflected. So here this big lens is the concave mirror, which plays a role of the objective lens that we saw last time.
01:10
Where this secondary lens would then converge the image through the eyepiece and get to your eyes.
01:24
And the second configuration, very similarly, is shown on the right. All right, so what's relevant for most of you who may one day become a doctor is a telescope or microscope, sorry.
01:45
So the configuration of a microscope is very similar to the telescope that we saw last time, which consists of an objective lens and an eyepiece, which is shown on this figure here. But what is the difference compared to the telescope situation that we discussed last time?
02:14
So now the object is much closer, right? Instead of observing a distant star, now the object
02:21
is much closer and the objective image is no longer at the focal plane of the objective lens. All right, so instead of forming an image at the focal plane of the objective lens, right now, I mean in this case, the image, the objective image is from right here.
02:44
This is denoted by I1, which is the objective image. Is the microphone on? Yes? All right. And then this image is viewed through the eyepiece. So the final image, once again,
03:02
is virtual and it is inverted and it is formed at this location, denoted by I2. All right, so what is the magnification in this case? The magnification depends upon two factors. First of all, the first image, the objective image, gets magnified.
03:28
So there is a magnification factor associated with this first image. And that's given by M0, which is a ratio of HI, the size of the image, divided by the size of the object.
03:45
And we already derived last time, this is given by D sub I, the distance between the image and the lens, to the distance of the object. And what does this negative sign tell us? It is inverted.
04:05
All right, so practically, the lens between the objective lens and the eyepiece, which is denoted by L in this diagram, is much larger compared to the focal lenses of the objective lens and the eyepiece.
04:27
So in this case, we can approximate it, D0, the distance of the object to the objective lens, roughly as the focal lens of the objective lens.
04:45
And this distance, D sub I, can be approximated as L minus FE, which is the focal lens of the eyepiece. So I just put that back into this expression. This is the final result for the first magnification factor.
05:07
Any questions about this? All right, and similarly, once this image gets through the eyepiece, there's a second magnification factor, which is given by the
05:20
near point distance N, which is once again 25 centimeters for normal human eyes, divided by the focal lens of the eyepiece. So what is the total magnification? That would be the products of the two factors.
05:42
All right, so the total magnification is then the products of the two magnification factors, where we already said this big M sub E, which is a magnification due to the eyepiece, is given by the normal lens divided by the focal lens of the eyepiece.
06:04
So that's where this N divided by FE factor comes from, where this little M0 is given by L minus FE divided by FE. And once again, this holds because the distance between the two lenses is much bigger compared to the two focal lenses.
06:26
So after some simplification, this is your final result. Any questions? All right, first of all, let's look at one example.
06:44
Suppose you have a compound microscope, as we discussed just a minute ago, which consists of 10 times eyepiece and 150 times objective lens, and these two lenses are 17 centimeters apart.
07:03
So what does this two information tell you? This would correspond to the two magnification factors, right? One is little M0, the other is big M0. And what is this 17 centimeters? This would be the L, distance L, that we denoted on this figure.
07:30
Correct? All right, so the question is, what is the overall magnification? Right, that would be the product of these two magnification factors, which give you 500. That's simple.
07:46
All right, so part B, what are the focal lenses of these two lenses? Namely, what is F of E, the focal lens of the eyepiece, and what is the focal lens of the objective lens?
08:02
And the third part, what is the position of the object when the final image is in focus with the eye relaxed? All right, so how do you proceed? So first of all, to find out the focal lens of the eyepiece, remember, it
08:29
is given by the ratio of the near point distance, 25 centimeters, divided by epsilon E. So if I move epsilon E to the other side, given that now I know the magnification factor associated with the eyepiece, which is what?
08:54
Which is 10 times, right? So it just takes 25 centimeters divided by 10, that would give me the focal lens of the eyepiece.
09:07
Yeah? Epsilon E. So once again, I'm just reversing this, inverting this equation. So I move epsilon E, which is the focal lens of the eyepiece, to the other side, and this magnification factor will be downstairs.
09:30
Right? Any questions? This is good? All right, so I just make use of this relation.
09:43
That will tell me the focal lens of the eyepiece. So once I know that, I can then go ahead and calculate the distance of the object, D sub zero. Making use of this equation, so once again, where does this equation come from?
10:03
They come from this equation, which tells me m zero, little m zero, which is the magnification due to the objective lens. It is given by minus L, which is the distance between the two lenses minus the focal lens of the eyepiece, divided by the object distance, D zero.
10:31
Right? So now what are the nulls in this equation? Do we know little m zero? Yes, what is it? It's 50, right? Given in the equation.
10:50
So I know little m zero, and what else do I know? L is null, it is 17 centimeters, which is the distance between the two lenses.
11:03
And m sub e is null, because we just calculated in part A. So you can then go ahead and calculate D zero, you just solve for D zero. Right? You have one equation, one unknown, you can find out what that unknown is. All right, so we just plug everything in. This is the final result, 0.29 centimeters.
11:26
But once you know this information, you can then go back and calculate what the focal lens of the objective lens is. By making use of this relation, which tells you, D sub i, this is the distance between the
11:43
image and the lens, is given by L minus F e, which is once again shown on this diagram. Right? And then using the lens equation, you can then find out what the focal lens of the objective lens is.
12:07
Any questions? All right, so this is good. All right, so the very last topic before we move on to interference is the lens imperfection.
12:27
So if I just handed out a lens, it's never perfect. It's the real world. And as it turns out, these imperfections can arise in three ways.
12:44
So the first imperfection, this is called the spherical aberration, which is due to the fact that the rays that come through the lens, they are not really focused exactly at one point.
13:01
All right, so as shown on this figure, what you see is for those rays that come through closer to the center of the spherical lens, they are more focused. However, for those rays that go to the edges of the spherical lens, they are not exactly focused at the same point.
13:28
So this is called the spherical aberration. So how do you avoid such imperfection?
13:42
So just to tell you, this imperfection arises because the light rays that go toward or go closer to the edge of the spherical lens, they don't really get focused at the same point. So in order to avoid this imperfection, one way to do it is to just make use of the central piece or central part of the spherical lens.
14:07
Or you can also make use of a spherical lens. All right, so the second way that this imperfection can arise is called the distortion.
14:24
So this is indicated in this second figure. Basically this arises because for rays that go, I mean, for rays that is at different distance from the axis, they don't get the same magnification factor.
14:46
Is it clear? So you have a center axis of the lens, but for light rays that are at different distances from this axis, they get magnified by different factors. And therefore, you could get distortions in these two fashions.
15:08
So there are actually applications of such distortion. And you all see these so-called fish eye pictures. This special lens is used for camera, which you take a photograph, which may lead to such distortion.
15:26
All right, so the third way this imperfection can arise, and this is called the chromatic aberration. Basically this is a dispersion effect, and the basic reason for this
15:44
imperfection is the fact that the index of refraction depends upon the wavelength. All right, so what that means is if you pass through the white light, through the lens, and remember the white light would include many, many different wavelengths.
16:04
For different wavelengths of light, they see a different index of refraction. And therefore, different colors of light rays, they don't get focused at the same point. All right, so this is the third way the imperfection can arise.
16:25
So this would conclude chapter 33, and we can move on to interference.
16:58
So recall that the light has a dual nature.
17:02
It could either be interpreted as particles or waves. This is the dual nature of light. The wave nature of light is manifest in three ways.
17:23
One is interference. The second phenomena, which is associated with the wave nature of light, is called the diffraction.
17:48
And the third manifestation of the wave nature is polarization. So we'll go through this one by one. So let's recall if you have two mechanical waves that interfere constructively.
19:20
All right, so here are the two mechanical waves, and let's for simplicity assume that both mechanical waves have the same amplitude, A. So what happens if these two mechanical waves interfere constructively?
19:41
Cancels. Cancels? Doubles. Doubles, right. So what that means is the amplitude of the final result gets doubled. So after a constructive interference, algebraically you just add up the two
20:06
wave functions, and the final result would have amplitude twice the original amplitude.
20:30
So amplitude increases.
20:48
Then if these two mechanical waves have destructive interference, you knew the answer. Cancels. They cancel. So for that to happen, what does that mean by destructive interference?
21:25
So suppose that's the first mechanical wave, Y1. How does Y2 look like? Half of the wave runs away, right? In other words, that would be the second mechanical wave at this moment.
21:53
And what is the total wave function? They cancel, so it just, there's no amplitude at all.
22:02
Or no displacement at all, sorry. So in these two examples here, we have made a very important assumption.
22:21
Namely, the phase difference between these two mechanical waves is a constant. What is the phase difference in the first case when there's constructive interference? Zero. Very good. And how about the second situation when there's completely destructive interference?
22:47
Or equivalently, it's half of the wavelength.
23:20
So the condition for interference, observable interference, is that the source must be coherent.
23:52
Meaning there's a constant phase. Right?
24:18
Which is, I mean, here I give you two simple examples.
24:22
Where these two mechanical waves must have constant phase relation. So similarly, with a light ray, or two light rays, in order for interference to occur, those two sources, light sources, must have constant phase relation. The second condition for interference to occur is that the source must be monochromatic.
24:58
What does that mean?
25:02
Means the light source must have one single wavelength.
25:47
So in the so-called double slit experiment, or Young's experiment, which is the experiment that shows the wave nature of light, has the following setup.
26:07
So on the left, you have some monochromatic light source. Once again, that's a light source that has a single wavelength passing through double slits.
26:33
So once the light reaches the double slit, each of those two slits will serve as a light source.
26:43
In other words, each of the slits will serve as a point light source.
27:03
It needs spherical light wave. So these light waves coming out of this two point light source will of course propagate.
27:21
And at some distance away, you have a screen right here. And on this screen, you will be able to observe the interference patterns due to the waves coming out of these two light sources. So S1 and S2 here serve as two coherent light sources.
28:07
And on the screen, which is a distance L away, one will be able to observe the interference pattern.
28:32
So what happened at the location, which is along the central axis on the screen?
28:40
What would be the pattern observed there? Destructive? How do you find that out? To answer that question, we need to know how far, what is the distance the light wave travels.
29:18
Actually, let me not draw this.
29:34
So suppose the light wave that travels from source S1 to point P is given by R1.
29:46
And the wave that travels from S2 to point P, the distance is R2. So what's the relationship between these two distances if P is located at the center, the symmetric point?
30:04
They will be the same. So is there a constructive or destructive interference? There will be constructive interference. So what happened? What do you expect? Do you expect to see a bright spot or a dark spot? They will be bright. Right? Because that's constructive interference.
30:32
So again, suppose this is point P, which is located right at the center, the symmetric point.
30:57
What you expect is R1 and R2 are exactly the same.
31:01
And therefore, these two waves must interfere constructively. And therefore, you expect to observe a bright spot.
31:40
So now let's move away from the center downward to some distance which is at location Q here. And suppose the two waves originated at these two sources, they differ by half of the wavelength.
32:06
So in other words, R1 is half of a wavelength more compared to R2.
32:45
Then what kind of interference pattern do you expect? Destructive. Destructive. And so you would expect to observe a dark spot.
33:01
Say it again? Isn't S1? No, so they originally, I mean they get originated. I'm actually plotting the distance. This is distance, so this is where Q located.
33:26
Alright, and this is where Q is located. Because I mean you have the wave continuously feeding in, right? Does that make sense? Yeah? Alright, so in this case, at the point Q, these two waves are out of phase.
33:45
Right, they differ by half wavelength or pi. And therefore, this is destructive interference and you expect to observe a dark spot.
34:03
So let's just see. So now Ben is going to shine a monochromatic light source which is laser. It's a very good light source which has only one single wavelength and it's coherent. And the light would then pass through a double slit.
34:23
And here's a screen which is very far away from the slit. So let me just try to, don't walk on the stairs, otherwise you may fall. So can everybody see the pattern? So what happened right in the middle? Is it bright or dark?
34:43
Bright. And some distance away, to the right, you see a complete dark spot. And actually, how many do you see? Many.
35:01
So actually what you observe is they are actually, for each bright fingers, you actually see many dark in between. So in other words, there are interference patterns within interference patterns. Right, so we'll get more into it when we discuss diffraction.
35:23
But everybody observe the dark spot like some distance away from the center, right? Yes or no? Yes. Alright, very good. Thank you. Okay, so quantitatively, what are the locations where all these dark spots are located?
35:48
So let's suppose that the distance between these two slits is given by d, little d.
36:33
Alright, so once again, this is the distance between the two slits. And some distance away, or some distance away, we have our screen.
36:50
So suppose at this point, which is the distance y above the central axis.
37:01
And this is a location where we observe, let's see, which kind of spot do we want. Let's not specify it, but just set up our coordinates first. Alright, so suppose this is the point of interest, which is some distance y above.
37:25
Then in order to find out what kind of interference pattern that is observed at this location, we need to know the past differences between the two waves originated from these two sources, right?
37:46
Alright, so let's do that.
38:00
In other words, if I know the difference between this distance r2 and r1, that would tell me the phase difference between the two waves. Yes? And if the difference is integral multiple of the wavelengths, what do you expect?
38:24
What kind of interference pattern? Integral multiple of a wavelength. Either zero or one wavelength or two wavelengths. What kind of interference pattern do you expect?
38:40
Inter constructive, right? So let me just write that down. Alright, so I'm going to code the past difference.
39:03
I code it delta, which is r2 minus r1. And if this value is integral multiple of a wavelength, then we expect constructive interference and therefore a bright spot.
39:40
And m here is an integer. It can be zero, one, two, etc. Any questions about this? This is good? Alright, and similarly for destructive interference, the value for delta, half of the wavelength.
40:23
So in other words, this would be lambda multiplied by some integer plus one half, right?
40:40
It's either one half or three half or five half. That would give you destructive interference. And m here, once again, is some integer.
41:05
For the case when this screen is very far away from the two slits, as what we just saw in the demonstration, these three light rays are approximately parallel.
41:24
Everybody agree with this statement? Right, if I keep moving the screen in this direction, those three lines I drew look like as though they are parallel. So we can simplify our geometry a bit.
41:43
Let's see. Once again, if the distance between the screen and the two slits is very far away,
42:01
then these three lines are as though they are parallel,
42:22
and that would allow me to write down delta in a simple form. So this is R1, L, and R2.
42:40
Alright, so suppose this angle here, which specifies the location on the screen, is given by theta. So you all agree that for a particular distance above or below the central axis,
43:04
there is a corresponding theta angle, right? And how do you write down theta? So theta, if it's small enough, this is given by y divided by L for small angles.
43:35
So if this angle is theta, which specifies the location on the screen,
43:41
then I know this angle is also theta. If you don't agree, just go home and draw the picture nicely and convince yourself. Alright, so the past differences.
44:05
Delta is nothing but this distance, and remember this is 90 degrees. So this distance will give me delta. And how do you express delta in terms of this angle?
44:24
D sine theta. Very good. Alright, so I think probably let's stop here and then continue Friday.