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Refractive Lenses and Image Formation

00:00:11.17 00:00:13.16 Light microscopes require lenses
00:00:13.17 00:00:15.12 in order to produce magnified images
00:00:15.13 00:00:19.06 and capture details within samples.
00:00:19.07 00:00:21.04 Now the tremendous improvement
00:00:21.05 00:00:23.06 and capabilities of microscopes
00:00:23.07 00:00:24.24 of the last 300+ years
00:00:24.25 00:00:28.09 is a result of detailed knowledge of light,
00:00:28.10 00:00:31.21 of lens material, and of how those two interact
00:00:31.22 00:00:34.06 to produce high quality images.
00:00:34.07 00:00:35.09 So in order to understand
00:00:35.10 00:00:36.16 what's inside of a microscope
00:00:36.17 00:00:39.22 and to understand how to use a microscope
00:00:39.23 00:00:40.29 to the best of its abilities,
00:00:41.00 00:00:43.07 and to figure out how to innovate
00:00:43.08 00:00:45.01 to produce new imaging capabilities,
00:00:45.02 00:00:48.08 one needs to know the fundamentals of light,
00:00:48.09 00:00:49.24 lenses, and image formation.
00:00:49.25 00:00:54.07 So this lecture will talk about four main topics:
00:00:54.08 00:00:56.12 I'll start with the properties of light
00:00:56.13 00:00:59.06 en what they are, how they are involved in
00:00:59.07 00:01:03.05 moving through optical systems
00:01:03.06 00:01:05.01 Next I'll talk about light-matter interactions,
00:01:05.02 00:01:07.07 the very simple and basic concepts of
00:01:07.08 00:01:09.26 reflection and refraction.
00:01:09.27 00:01:12.01 And then we will focus on refractive lenses,
00:01:12.02 00:01:13.21 those are the kinds of lenses that
00:01:13.22 00:01:15.24 most light microscopes use
00:01:15.25 00:01:20.07 to guide light directly and use it to form images.
00:01:20.08 00:01:21.23 And finally we will talk about
00:01:21.24 00:01:24.00 the details of image formation
00:01:24.01 00:01:26.09 and some of the things to watch out for
00:01:26.10 00:01:29.19 as well as some of the possibilities with those.
00:01:29.20 00:01:32.13 OK. So let's start with the big picture
00:01:32.14 00:01:34.24 and that is the electromagnetic spectrum.
00:01:34.25 00:01:36.01 The light that we see,
00:01:36.02 00:01:37.22 the light that's coming into our eyes
00:01:37.23 00:01:41.16 is the result of electromagnetic waves
00:01:41.17 00:01:45.24 of only a small bit of which we can detect.
00:01:45.25 00:01:47.16 And that is the visible spectrum
00:01:47.17 00:01:49.21 Uh, the visible spectrum here.
00:01:49.22 00:01:51.25 Each of those wavelength
00:01:51.26 00:01:53.26 has a number of different properties.
00:01:53.27 00:01:56.03 And you can think about a light wave
00:01:56.04 00:02:00.24 as being a sinusoidal entity.
00:02:00.25 00:02:02.20 But that sinusoid is not something that is
00:02:02.21 00:02:05.21 physically oscillating up and down
00:02:05.22 00:02:09.00 Rather, when light is described as a wave or
00:02:09.01 00:02:12.23 is indicated as this sinusoidal pattern,
00:02:12.24 00:02:13.23 what that is referring to is
00:02:13.24 00:02:15.16 the electro field intensity.
00:02:15.17 00:02:17.06 So along a given position
00:02:17.07 00:02:19.08 there is the electro field intensity,
00:02:19.09 00:02:21.12 that varies in space and in time.
00:02:21.13 00:02:23.06 It's a harmonic wave.
00:02:23.07 00:02:24.27 And so there are a number of different properties
00:02:24.28 00:02:26.28 that each wave has.
00:02:26.29 00:02:29.18 It has wavelength, denoted by lumda,
00:02:29.19 00:02:30.25 It has an amplitude,
00:02:30.26 00:02:32.05 and that amplitude is the
00:02:32.06 00:02:34.18 magnitude of the electric field
00:02:34.19 00:02:38.12 or could be the magnitude of the magnetic field.
00:02:38.13 00:02:40.04 It has a frequency of oscillation,
00:02:40.05 00:02:42.24 so how fast over time is it moving?
00:02:42.25 00:02:44.16 It also has a translation speed.
00:02:44.17 00:02:47.19 So this is a moving electromagnetic wave,
00:02:47.20 00:02:49.20 propagating wave.
00:02:49.21 00:02:51.19 And so that wave has a speed.
00:02:51.20 00:02:53.04 It also has a phase.
00:02:53.05 00:02:56.14 So it has eh, its peaks and trough.
00:02:56.15 00:02:59.02 So the wave relative to some reference point
00:02:59.03 00:03:04.16 move through 0 to 360 degrees.
00:03:04.17 00:03:06.06 It also has polarizations.
00:03:06.07 00:03:07.07 So an orientation to
00:03:07.08 00:03:09.24 that electric field that's oscillating.
00:03:09.25 00:03:12.28 Some of these properties of waves are interrelated.
00:03:12.29 00:03:15.07 So for example, speed is the product of the
00:03:15.08 00:03:16.25 wavelength and the frequency.
00:03:16.26 00:03:20.06 Those are connected by the speed of light.
00:03:20.07 00:03:22.10 So let's give a practical example.
00:03:22.11 00:03:23.08 Most people have,
00:03:23.09 00:03:26.07 had to work with laser pointers before.
00:03:26.08 00:03:28.07 So let's take a typical laser pointer that
00:03:28.08 00:03:33.06 has a wavelength of about 635 nm.
00:03:33.07 00:03:35.08 And you can read on most laser pointers
00:03:35.09 00:03:36.07 what is their power.
00:03:36.08 00:03:39.03 And let's take one that has two milli Volts of power.
00:03:39.04 00:03:42.10 If you measure the area of the beam that coming out
00:03:42.11 00:03:44.23 that's one more property of this laser pointer
00:03:44.24 00:03:46.21 and then let's take something that other
00:03:46.22 00:03:49.24 people have measured and that is the speed of light.
00:03:49.25 00:03:52.07 so if we take those four pieces of data,
00:03:52.08 00:03:54.19 we can work out a few different properties
00:03:54.20 00:03:58.26 of the waves that are coming out of our laser pointer.
00:03:58.27 00:04:02.09 For one, we can calculate the intensity of the wave.
00:04:02.10 00:04:04.15 If we take the power that's coming out,
00:04:04.16 00:04:07.09 then divided by the area, we get intensity.
00:04:07.10 00:04:09.05 That's a common measure of light
00:04:09.06 00:04:11.28 passing through any imaging system.
00:04:11.29 00:04:14.19 That is how much power per unit area
00:04:14.20 00:04:16.07 or intensity is present.
00:04:16.08 00:04:17.13 And for a laser pointer,
00:04:17.14 00:04:20.19 that's a relatively large 250 Volts per meter squared.
00:04:20.20 00:04:24.08 Amplitude, so amplitude of the electric field.
00:04:24.09 00:04:29.08 What is that field locally at the, along
00:04:29.09 00:04:31.14 the beam of laser coming out of the laser pointer?
00:04:31.15 00:04:34.09 That, if you calculate that.
00:04:34.10 00:04:38.13 That's proportional to the square root of the intensity.
00:04:38.14 00:04:41.02 And that ends up being 430 Volts per meters.
00:04:41.03 00:04:44.03 And then we can calculate the frequency
00:04:44.04 00:04:47.11 If we know that this is a laser that propagating in air,
00:04:47.12 00:04:50.27 we can take the speed of light in air,
00:04:50.28 00:04:53.14 and divide that by the wavelength
00:04:53.15 00:04:57.12 and get a frequency in one of a seconds, or Hertz.
00:04:57.13 00:05:01.06 And that ends up being a very very large number.
00:05:01.07 00:05:05.06 So that's frequency, intensity, amplitude.
00:05:05.07 00:05:07.25 Now what happens when that lights
00:05:07.26 00:05:10.06 interfaces with another material?
00:05:10.07 00:05:12.07 So the speed of light in vacuum
00:05:12.08 00:05:14.10 is a fixed well known number.
00:05:14.11 00:05:17.16 And as soon as you pass light through other materials
00:05:17.17 00:05:20.05 it turns out that light slows down
00:05:20.06 00:05:24.06 and light slows down in proportion to a number,
00:05:24.07 00:05:26.05 that is now known as the index refraction.
00:05:26.06 00:05:29.04 So if you measure speed of lights in a material,
00:05:29.05 00:05:32.25 if you compare that to the speed of lights in vacuum,
00:05:32.26 00:05:34.14 the ratio of those two is this index.
00:05:34.15 00:05:37.17 So index of refraction has been quantified
00:05:37.18 00:05:39.20 for a wide range of materials
00:05:39.21 00:05:41.01 and is one of those important properties
00:05:41.02 00:05:44.16 of lenses that are using in imaging systems.
00:05:44.17 00:05:47.16 And what you will notice from the diagram here
00:05:47.17 00:05:51.20 is that the amplitude has remained
00:05:51.21 00:05:53.29 quite large in this particular material
00:05:54.00 00:05:57.28 but the distance between the peaks
00:05:57.29 00:05:59.06 and troughs has reduced.
00:05:59.07 00:06:01.18 And what that means is that
00:06:01.19 00:06:03.29 the waves speed is slowing down
00:06:04.00 00:06:07.21 it also means that the wave length is getting smaller
00:06:07.22 00:06:10.11 as it passes through this higher indexed material.
00:06:10.12 00:06:12.28 And that wavelength is recovered and
00:06:12.29 00:06:15.18 the speed is recovered as it exits the material.
00:06:15.19 00:06:20.17 And so what this tells us is that the properties of lights
00:06:20.18 00:06:23.27 change as you move from one material to another
00:06:23.28 00:06:25.19 so you have to know what material you are in
00:06:25.20 00:06:29.25 in order to be able to define well the properties of lights.
00:06:29.26 00:06:34.17 OK. When we make drawing of
00:06:34.18 00:06:36.22 lights or when we talk about it
00:06:36.23 00:06:39.23 often times we don't use the wave representation
00:06:39.24 00:06:42.00 even though that's the more accurate way to think about
00:06:42.01 00:06:44.27 light as being this propagating wave.
00:06:44.28 00:06:46.16 Often times it's more convenient
00:06:46.17 00:06:48.15 to simply denoted it as an arrow
00:06:48.16 00:06:51.02 or sometimes to indicate wave fronts.
00:06:51.03 00:06:55.03 And so wave front would be positions of constant phase.
00:06:55.04 00:07:00.05 Now the reason why this is convenient is the drawing is easier
00:07:00.06 00:07:02.05 but it also makes sense because the frequencies
00:07:02.06 00:07:04.07 are extraordinary high
00:07:04.08 00:07:06.23 as we calculate for a laser pointer
00:07:06.24 00:07:09.27 frequencies on the scale of ten to the fourteen Hertz is
00:07:09.28 00:07:14.08 much faster than we see, much faster than most detectors.
00:07:14.09 00:07:18.08 So what is most relevant is typically the intensity of light
00:07:18.09 00:07:21.17 and the wavelength the material that it is in.
00:07:21.18 00:07:24.18 So typically that could be related simply by arrows.
00:07:24.19 00:07:26.15 So there are multiple ways of referring to
00:07:26.16 00:07:28.06 light passing through materials
00:07:28.07 00:07:31.13 and we will take advantage of several of them.
00:07:31.14 00:07:34.17 So let's move now to light-matter interaction.
00:07:34.18 00:07:37.21 and specifically what happens at interfaces.
00:07:37.22 00:07:40.09 We have already learnt that lights slows down
00:07:40.10 00:07:42.10 when it enters a higher index material.
00:07:42.11 00:07:45.14 But what happens to the angle of light
00:07:45.15 00:07:48.28 if that light enters the material with an angle?
00:07:48.29 00:07:52.26 So here what is being shown here is an incident wave.
00:07:52.27 00:07:54.17 The incident wave is making contacts
00:07:54.18 00:07:57.12 with a higher index material
00:07:57.13 00:08:02.09 so the material below has a slower wave speed.
00:08:02.10 00:08:04.05 Two things will happen.
00:08:04.06 00:08:06.11 One, it's observed and you can see
00:08:06.12 00:08:09.13 this when you look at a window
00:08:09.14 00:08:13.06 that has light shining on it that you'll get a reflection.
00:08:13.07 00:08:15.26 So that reflection is something that
00:08:15.27 00:08:21.18 occurs from the surface of this material.
00:08:21.19 00:08:24.16 But you'll also get light that's propagating through the material.
00:08:24.17 00:08:27.29 And so this, the slice that's propagating through,
00:08:28.00 00:08:28.26 transmitted through,
00:08:28.27 00:08:31.08 is called refractive wave.
00:08:31.09 00:08:33.16 You might notice that there is a kink
00:08:33.17 00:08:35.29 in the incident wave to refractive wave.
00:08:36.00 00:08:38.10 That's because the angle which that
00:08:38.11 00:08:40.17 wave propagates through the material
00:08:40.18 00:08:45.04 has been found to depend both on the angle of indents
00:08:45.05 00:08:48.23 as well as the index refraction of the two materials.
00:08:48.24 00:08:53.12 Now we can draw this as a series of rays
00:08:53.13 00:08:56.09 but we can also denote this as a series of wave fronts.
00:08:56.10 00:09:00.21 So if we think about waves constant wavefronts coming in
00:09:00.22 00:09:03.02 this is another way to designate
00:09:03.03 00:09:04.27 how this interaction is taking place.
00:09:04.28 00:09:08.02 So the relationship that has been observed
00:09:08.03 00:09:13.02 has been formalized into laws of reflection.
00:09:13.03 00:09:15.06 The law of reflection simply says
00:09:15.07 00:09:17.26 for a given material, given interface,
00:09:17.27 00:09:22.09 the angle of incidents is equal to the angle of reflection.
00:09:22.10 00:09:25.26 Conversely, for the refraction,
00:09:25.27 00:09:27.28 it depends on the index of the material.
00:09:27.29 00:09:33.18 So where lights will go depends on the angle of incidents
00:09:33.19 00:09:36.21 the sin of that, times the index refraction,
00:09:36.22 00:09:41.03 equals the same product in the transmitted medium.
00:09:41.04 00:09:44.17 Now these equations tell you something
00:09:44.18 00:09:47.03 very useful and very important about light.
00:09:47.04 00:09:50.15 They tell you where it's gonna go at any interface.
00:09:50.16 00:09:52.23 And these interfaces are assumed to be
00:09:52.24 00:09:56.06 smooth and specularly reflecting
00:09:56.07 00:10:00.09 so that's a caveat on this set of equations.
00:10:00.10 00:10:02.14 But the important point here is that
00:10:02.15 00:10:04.15 this tells us where the lights are gonna go.
00:10:04.16 00:10:06.20 But it doesn't tell us how much
00:10:06.21 00:10:09.05 So that's a second set of equations.
00:10:09.06 00:10:11.06 How much light is passing through
00:10:11.07 00:10:13.22 an interface depends on
00:10:13.23 00:10:17.04 a more extensive variation set of equations
00:10:17.05 00:10:19.10 called the, for now, reflection coefficient,
00:10:19.11 00:10:20.24 and transmission coefficients.
00:10:20.25 00:10:25.09 But the simplest possible case of lights hitting a material
00:10:25.10 00:10:28.21 normal at a right angle of the surface
00:10:28.22 00:10:31.02 you can make a quick estimate for how much
00:10:31.03 00:10:35.01 the intensity is going to be reflected
00:10:35.02 00:10:36.17 and how much of that intensity
00:10:36.18 00:10:38.21 is going to be transmitted through the material.
00:10:38.22 00:10:40.13 And if we take an example of
00:10:40.14 00:10:44.11 a glass at an air-glass interface,
00:10:44.12 00:10:49.05 given an index refraction of 1 for air and 1.5 for glass
00:10:49.06 00:10:50.26 about 4% of lights
00:10:50.27 00:10:53.27 is going to be bouncing back from that surface.
00:10:53.28 00:10:56.23 The rest will be transmitted,
00:10:56.24 00:10:59.13 assuming that there is no absorption.
00:10:59.14 00:11:03.14 So we are gonna take a moment and do a quick demo
00:11:03.15 00:11:06.26 about how this manifest itself
00:11:06.27 00:11:08.22 for a couple of different materials
00:11:08.23 00:11:11.27 using a light source and a detector to measure
00:11:11.28 00:11:14.08 how much intensity is passing through them.
00:11:14.09 00:11:18.13 So with this demo, what I want to do is
00:11:18.14 00:11:19.06 introduce some concepts
00:11:19.07 00:11:21.22 about light-matter interaction
00:11:21.23 00:11:24.12 and specifically, the effect of wavelength.
00:11:24.13 00:11:25.22 So we'll start with,
00:11:25.23 00:11:29.18 with a nice clear piece of quartz.
00:11:29.19 00:11:31.17 It's even be hard to see,
00:11:31.18 00:11:34.06 but there is a real piece of quartz right here.
00:11:34.07 00:11:38.05 And what I've got are a light source,
00:11:38.06 00:11:39.21 so this is a Halogen lamp,
00:11:39.22 00:11:41.19 and I've got a little detector
00:11:41.20 00:11:44.17 so this thing right here is a detector that
00:11:44.18 00:11:48.08 measures how much intensity is
00:11:48.09 00:11:50.09 is presence on the face of this detector.
00:11:50.10 00:11:55.02 And we can read it out with this dial here.
00:11:55.03 00:11:57.17 so if you see that little red thing moving back and forth
00:11:57.18 00:12:00.23 that tells us how much light is hitting the detector.
00:12:00.24 00:12:04.00 Now this is transparent
00:12:04.01 00:12:06.21 so it means at least to our eyes, light can pass through it.
00:12:06.22 00:12:11.02 And we might expect if I put this in the path,
00:12:11.03 00:12:15.01 that my detector would not go down too much.
00:12:15.02 00:12:21.22 So if I move in the path, and move out, move in, move out
00:12:21.23 00:12:24.14 When I'm in you see a slight reduction
00:12:24.15 00:12:26.17 and that's because there is reflection
00:12:26.18 00:12:29.07 from both surfaces of the quartz.
00:12:29.08 00:12:31.02 but most of the light is getting through.
00:12:31.03 00:12:36.07 OK. So let's contrast this with this thing here.
00:12:36.08 00:12:39.11 So maybe you can see this a little easier.
00:12:39.12 00:12:41.00 It's highly reflective.
00:12:41.01 00:12:42.01 It's a piece of silicon.
00:12:42.02 00:12:46.00 And if I put my eye up to it and I try to look
00:12:46.01 00:12:47.15 I see nothing through it.
00:12:47.16 00:12:49.16 So I might expect when I
00:12:49.17 00:12:52.23 put this in between,
00:12:52.24 00:12:54.05 the light source and the detector
00:12:54.06 00:12:56.26 that I would extinguish all the intensity
00:12:56.27 00:12:59.11 that I would block all the light.
00:12:59.12 00:13:03.12 So let's try that.
00:13:03.13 00:13:08.20 So now it's in and it's out. And it's in.
00:13:08.21 00:13:11.12 I don't know if you can see, but
00:13:11.13 00:13:14.00 the dial doesn't go all the way to 0.
00:13:14.01 00:13:15.22 It seems like there is still
00:13:15.23 00:13:18.08 some intensity entering into the detector.
00:13:18.09 00:13:20.28 Well maybe that's just room lights.
00:13:20.29 00:13:24.11 So let's add a piece of metal.
00:13:24.12 00:13:26.17 So this is just a piece of metal ruler.
00:13:26.18 00:13:31.20 And let's stick this also in the path of the detector.
00:13:31.21 00:13:34.26 Now it goes to 0.
00:13:34.27 00:13:37.26 So we didn't turn off the room light.
00:13:37.27 00:13:40.28 All I did was add one more thing
00:13:40.29 00:13:43.13 blocking the path of the ligth.
00:13:43.14 00:13:45.04 So why is that?
00:13:45.05 00:13:47.08 Well it turns out that silicon
00:13:47.09 00:13:49.04 while it's opaque to our eye,
00:13:49.05 00:13:51.00 is not opaque to the lamp.
00:13:51.01 00:13:53.19 And that's because the lamp, a Halogen lamp,
00:13:53.20 00:13:56.25 producing infrared electromagnetic waves,
00:13:56.26 00:13:58.29 in addition to visible light.
00:13:59.00 00:14:02.05 And that infrared, longer wavelength, lower energy,
00:14:02.06 00:14:05.13 is, can transmit through silicon.
00:14:05.14 00:14:08.12 And as a result of the transmission,
00:14:08.13 00:14:10.25 this to infrared wavelength,
00:14:10.26 00:14:15.13 silicon appears like quartz does to our eye.
00:14:15.14 00:14:17.23 Transparent.
00:14:17.24 00:14:20.21 And in fact, if you build an infrared microscope,
00:14:20.22 00:14:26.14 some infrared microscopes use lens made of silicon.
00:14:26.15 00:14:27.26 So now we understand what happens
00:14:27.27 00:14:30.26 when light interacts with an interface,
00:14:30.27 00:14:32.20 we can begin to understand
00:14:32.21 00:14:34.23 what happens at sets of surfaces.
00:14:34.24 00:14:37.02 more specifically, at lenses,
00:14:37.03 00:14:38.15 which have two surfaces.
00:14:38.16 00:14:41.29 We can think about the bending of the lights
00:14:42.00 00:14:43.26 at each surface independently.
00:14:43.27 00:14:47.20 So each interface will follow the same set of laws,
00:14:47.21 00:14:50.24 the law of reflection, and the law of refraction.
00:14:50.25 00:14:53.02 And that means what we need to know
00:14:53.03 00:14:55.04 in order to determine where the light would go
00:14:55.05 00:14:57.22 as it hits the lens,
00:14:57.23 00:14:59.19 is to know where the normal is ? that surface
00:14:59.20 00:15:03.00 and to be able to work out from the law of refraction,
00:15:03.01 00:15:06.01 what angle the transmitted light will make.
00:15:06.02 00:15:08.07 If we do that for both surfaces,
00:15:08.08 00:15:09.15 we can figure out where
00:15:09.16 00:15:12.29 lights coming into a chunk of material,
00:15:13.00 00:15:15.02 like a lens, where it will end up.
00:15:15.03 00:15:17.29 And if you design that material properly,
00:15:18.00 00:15:20.06 then you can end up by controlling
00:15:20.07 00:15:22.10 where those light waves go,
00:15:22.11 00:15:24.09 where the rays go and where they end up.
00:15:24.10 00:15:27.27 Here's an example of a simple positive lens
00:15:27.28 00:15:30.27 in which there is refraction at the two surfaces
00:15:30.28 00:15:34.28 and if you have an entire beam passing into this lens,
00:15:34.29 00:15:37.28 a beam like from a laser pointer,
00:15:37.29 00:15:41.28 all of those rays which are entering parallel
00:15:41.29 00:15:44.06 will converge to a single spot,
00:15:44.07 00:15:46.08 and that's called the focal point.
00:15:46.09 00:15:48.26 And that focal point resides on a plane,
00:15:48.27 00:15:50.05 called the focal plane,
00:15:50.06 00:15:52.25 that is a distance f
00:15:52.26 00:15:56.04 or one focal length away from the lens.
00:15:56.05 00:15:59.25 Now this is the proper way to think about
00:15:59.26 00:16:02.00 light passing through lens
00:16:02.01 00:16:04.15 but for people who want to
00:16:04.16 00:16:07.09 prototype optical systems or
00:16:07.10 00:16:10.23 get a quick estimate for how a system is working
00:16:10.24 00:16:13.07 often times we use simpler equations,
00:16:13.08 00:16:15.25 and a simple equation shown here at the bottom,
00:16:15.26 00:16:17.18 that's the Lensmaker's equation.
00:16:17.19 00:16:19.04 And that Lensmaker's equation
00:16:19.05 00:16:21.12 has two important simplifications.
00:16:21.13 00:16:25.07 Number one, it assumes that the distance between
00:16:25.08 00:16:28.04 the two surfaces of the lens are very small,
00:16:28.05 00:16:29.27 so small as to be negligible.
00:16:29.28 00:16:33.17 So we don't actually need to follow the light
00:16:33.18 00:16:35.19 as it moves between one surface to another.
00:16:35.20 00:16:38.24 The second important simplification of maker's is that
00:16:38.25 00:16:42.06 the surfaces can all be described by spheres.
00:16:42.07 00:16:44.02 That is that they can all be described by a
00:16:44.03 00:16:45.24 single number of radius of curvature.
00:16:45.25 00:16:48.05 So once you know the radius of the curvature,
00:16:48.06 00:16:51.00 of the two surfaces of your lens,
00:16:51.01 00:16:52.09 and you know the index of the lens,
00:16:52.10 00:16:53.26 that's the n in the equation,
00:16:53.27 00:16:57.04 you can calculate how far away
00:16:57.05 00:17:00.14 parallel rays entering this lens will converge,
00:17:00.15 00:17:01.21 and that's the focal length.
00:17:01.22 00:17:03.11 This is a very powerful equation
00:17:03.12 00:17:07.18 because it gives us a very simple way of determining
00:17:07.19 00:17:09.15 or designing what a lens should do,
00:17:09.16 00:17:11.26 and putting together simple systems.
00:17:11.27 00:17:13.21 As we'll talk about in a moment,
00:17:13.22 00:17:16.26 there are a number of caveats for this simple equation.
00:17:16.27 00:17:18.16 Things that aren't captured.
00:17:18.17 00:17:22.13 But for the purposes of designing systems and
00:17:22.14 00:17:24.25 understanding how images are formed,
00:17:24.26 00:17:27.03 this simple set of equation is very useful.
00:17:27.04 00:17:32.02 Now lens comes in many different shapes and sizes.
00:17:32.03 00:17:35.03 The one I showed you just before was a,
00:17:35.04 00:17:37.02 called a plano-convex lens.
00:17:37.03 00:17:39.21 And the plano is because of
00:17:39.22 00:17:42.05 one surface being a flat surface,
00:17:42.06 00:17:43.27 or a radius of curvature that's infinite.
00:17:43.28 00:17:48.15 And the second surface has a concave curvature.
00:17:48.16 00:17:50.15 Uh, plano-convex rather, a convex curvature.
00:17:50.16 00:17:51.28 And if you take,
00:17:51.29 00:17:55.18 if you imaging two spheres that intersect,
00:17:55.19 00:17:58.06 those two spheres intersecting
00:17:58.07 00:17:59.24 can intersect in various ways.
00:17:59.25 00:18:01.16 And each of these different intersections
00:18:01.17 00:18:03.05 will give you a different kind of lens.
00:18:03.06 00:18:07.00 So here are the range of the different lens shapes
00:18:07.01 00:18:08.08 that can be generated
00:18:08.09 00:18:10.25 simply by intersecting two spheres.
00:18:10.26 00:18:14.20 And if you have the correct sign notation
00:18:14.21 00:18:16.04 for your radius of curvature,
00:18:16.05 00:18:19.03 you can simply calculate what should that,
00:18:19.04 00:18:19.20 uh, where should the lens focus.
00:18:19.21 00:18:23.29 And one interesting thing we will get to it at the very end,
00:18:24.00 00:18:25.15 is that the focal length
00:18:25.16 00:18:27.27 doesn't always have to be a positive number.
00:18:27.28 00:18:29.19 It can sometimes be a negative number.
00:18:29.20 00:18:32.02 And when you have a negative focal length,
00:18:32.03 00:18:33.20 or a negative lens,
00:18:33.21 00:18:37.08 the place where your image shows up is different.
00:18:37.09 00:18:39.23 And the kind of image you will get is different as well.
00:18:39.24 00:18:43.00 But let's go back to the simple case of a thin lens
00:18:43.01 00:18:47.05 focusing a bundle of rays down to a point.
00:18:47.06 00:18:50.14 So the way of drawing this here is very much a point,
00:18:50.15 00:18:52.24 It seems to be infinitely small.
00:18:52.25 00:18:54.27 But it's worth remembering that
00:18:54.28 00:18:58.08 waves are not infinitely small
00:18:58.09 00:19:00.12 they have dimensions to them.
00:19:00.13 00:19:01.10 They have wavelength.
00:19:01.11 00:19:05.13 And if you were to zoom in on that focal point,
00:19:05.14 00:19:06.22 what does it really look like.
00:19:06.23 00:19:08.10 Does it really look like a point?
00:19:08.11 00:19:09.12 And the answer is no.
00:19:09.13 00:19:11.06 This has been well known for a number of years.
00:19:11.07 00:19:14.11 If you solve the full vector diffraction theories,
00:19:14.12 00:19:18.13 then you get a distribution of intensity that looks like this.
00:19:18.14 00:19:19.14 Looks rather complicated.
00:19:19.15 00:19:21.24 But there is a very important line
00:19:21.25 00:19:23.18 that's drawn right here in the middle
00:19:23.19 00:19:27.00 And if you look at the intensity profile along that line,
00:19:27.01 00:19:29.07 that's the so called airy disc,
00:19:29.08 00:19:31.14 which defines the point spread function of your system.
00:19:31.15 00:19:34.23 Now this is a topic that will be covered in
00:19:34.24 00:19:36.16 much greater depth in a different lecture.
00:19:36.17 00:19:39.28 But this is a simply reminder that
00:19:39.29 00:19:41.15 our simplifications are useful for
00:19:41.16 00:19:44.25 understanding how systems are set up,
00:19:44.26 00:19:48.23 but the detail of resolution and of image quality
00:19:48.24 00:19:52.07 often come down to diffraction level of facts,
00:19:52.08 00:19:54.07 such as those shown here.
00:19:54.08 00:19:57.01 A couple of other things that can
00:19:57.02 00:19:59.15 affect most often negatively
00:19:59.16 00:20:02.20 your imaging capabilities are aberrations.
00:20:02.21 00:20:05.11 And there are two main flavors of aberrations.
00:20:05.12 00:20:06.24 There are chromatic aberrations
00:20:06.25 00:20:09.11 and monochromatic aberrations.
00:20:09.12 00:20:12.16 So chromatic aberrations are, because that n,
00:20:12.17 00:20:17.00 that index refraction that defines our material properties,
00:20:17.01 00:20:20.09 that n happens to be a function of wavelength.
00:20:20.10 00:20:23.17 There is not a single index for a material.
00:20:23.18 00:20:25.28 The index of the material depends on
00:20:25.29 00:20:27.12 what wavelength you are passing through it.
00:20:27.13 00:20:30.11 So the index can be higher or lower
00:20:30.12 00:20:32.22 for two different wavelengths.
00:20:32.23 00:20:35.10 And therefore they will focus to different points
00:20:35.11 00:20:38.09 and correcting this has been a major challenge and
00:20:38.10 00:20:40.16 one of the major advances in light microscopy
00:20:40.17 00:20:42.25 over the last several decades.
00:20:42.26 00:20:46.17 So the second kind of aberration
00:20:46.18 00:20:49.01 is a monochromatic aberration.
00:20:49.02 00:20:50.03 Monochromatic aberrations are t
00:20:50.04 00:20:51.14 hose aberrations that occur
00:20:51.15 00:20:53.01 even if you only have one wavelength
00:20:53.02 00:20:54.27 passing through the material.
00:20:54.28 00:20:57.14 And an example of one of the five major
00:20:57.15 00:20:59.29 monochromatic aberrations is shown here.
00:21:00.00 00:21:02.11 This is spherical aberration.
00:21:02.12 00:21:05.16 And this comes from the fact that even though
00:21:05.17 00:21:08.09 spherical surfaces are the easiest to make,
00:21:08.10 00:21:12.11 the sphere is not the perfect focusing shape.
00:21:12.12 00:21:15.08 In fact you need a different shape, an aspherical shape,
00:21:15.09 00:21:18.08 in order to perfectly focus a given wavelength to a spot.
00:21:18.09 00:21:24.04 But for large focal length, sphere tend to do a very good job,
00:21:24.05 00:21:26.02 and spherical aberration is not as bad.
00:21:26.03 00:21:29.11 And so again the concept of thing lenses
00:21:29.12 00:21:30.20 where we only care about
00:21:30.21 00:21:32.25 the index and the radius of curvature
00:21:32.26 00:21:34.23 those concepts are still useful in
00:21:34.24 00:21:37.16 thinking about how imaging systems work.
00:21:37.17 00:21:45.09 OK. So let's build up our skills so we can actually identify
00:21:45.10 00:21:47.26 where the image of an object will show up
00:21:47.27 00:21:49.22 on one side of the lens.
00:21:49.23 00:21:53.23 So we're gonna learn three tools of the trade,
00:21:53.24 00:21:58.25 and those are ways of identifying where rays should go,
00:21:58.26 00:22:01.24 where these representative waves should go,
00:22:01.25 00:22:04.27 from a given point on an object.
00:22:04.28 00:22:07.05 So if you think about an object as something
00:22:07.06 00:22:10.29 that is scattering light or emitting light,
00:22:11.00 00:22:12.03 we have the option of picking
00:22:12.04 00:22:14.02 a number of different rays coming from that
00:22:14.03 00:22:16.03 and asking where those go.
00:22:16.04 00:22:18.05 So what we're gonna do is that we are gonna be smart about
00:22:18.06 00:22:21.08 picking rays that do things we know.
00:22:21.09 00:22:28.01 The first is that any ray that comes in parallel to the optical axis,
00:22:28.02 00:22:31.14 the optical axis is this line all the way
00:22:31.15 00:22:35.13 along the center of the imaging system.
00:22:35.14 00:22:39.05 That optical axis, uh, if the ray comes in parallel to it,
00:22:39.06 00:22:40.26 the ray should converge
00:22:40.27 00:22:44.04 through a positive lens through the focal point.
00:22:44.05 00:22:47.08 If the ray comes at an angle,
00:22:47.09 00:22:50.02 it will still converge through the focal plane,
00:22:50.03 00:22:53.08 but off set from the optical axis.
00:22:53.09 00:22:54.26 So that's one very helpful rule.
00:22:54.27 00:22:57.15 Parallel rays coming in go through the focus.
00:22:57.16 00:23:00.07 The second helpful rule is just the opposite of that.
00:23:00.08 00:23:03.22 If you have light coming from a focus,
00:23:03.23 00:23:07.11 it will leave this lens as parallel rays.
00:23:07.12 00:23:12.02 So you can imaging those are the case because you can run
00:23:12.03 00:23:14.15 these two diagrams if you flip them around.
00:23:14.16 00:23:15.05 They are the same.
00:23:15.06 00:23:20.02 So there is one last rule of thumb for ray tracing
00:23:20.03 00:23:23.13 and that is rays passing through the center of the lens
00:23:23.14 00:23:26.06 are not reflected.
00:23:26.07 00:23:28.28 So in reality they are refracted a little bit
00:23:28.29 00:23:30.28 but the reflection is opposite.
00:23:30.29 00:23:33.12 So bend it one way and you bend it back the other way,
00:23:33.13 00:23:36.19 so it comes out looking as if it hasn't been refracted at all.
00:23:36.20 00:23:38.06 So those three things,
00:23:38.07 00:23:41.02 rays coming in parallel passing through a focus,
00:23:41.03 00:23:44.16 rays coming from a focus come out parallel,
00:23:44.17 00:23:45.20 and any ray that passes through
00:23:45.21 00:23:47.29 the middle of the lens isn't bent at all.
00:23:48.00 00:23:50.06 So we can now use that to
00:23:50.07 00:23:53.21 figure out where should an image show up
00:23:53.22 00:23:55.28 if we have a lens in front of this object.
00:23:55.29 00:23:59.17 So we'll start by tracing a few rays.
00:23:59.18 00:24:03.24 So these rays are all coming from the tip of the object.
00:24:03.25 00:24:06.16 So let's take this, the middle ray.
00:24:06.17 00:24:08.26 So the middle ray is passing all the way
00:24:08.27 00:24:10.19 through the center of the lens,
00:24:10.20 00:24:14.05 and based on that rule number three we shouldn't bend it at all.
00:24:14.06 00:24:18.03 That ray should pass all the way through and continue going.
00:24:18.04 00:24:20.18 Now if you look at the bottom ray,
00:24:20.19 00:24:24.08 that bottom ray is coming from the tip of our object.
00:24:24.09 00:24:28.27 But we've chosen it so that it passes through the focal point
00:24:28.28 00:24:32.21 of our lens, so the front focal point of the lens.
00:24:32.22 00:24:35.29 And what that means is that when it hits the lens, we know
00:24:36.00 00:24:39.06 it must be coming parallel to the optical axis.
00:24:39.07 00:24:44.24 So the optical axis is this, again, this dotted line here.
00:24:44.25 00:24:47.24 So where those two rays converge,
00:24:47.25 00:24:51.06 that is where the tip of our image must be.
00:24:51.07 00:24:53.23 The rays that came from that tip,
00:24:53.24 00:24:56.19 the lenses converging them back to that tip,
00:24:56.20 00:25:00.04 and that's what allows us to do the imaging.
00:25:00.05 00:25:03.20 And that third ray is that that doesn't follow either of our rules
00:25:03.21 00:25:08.13 but we know that any light coming from that tip
00:25:08.14 00:25:12.23 must end up at its conjugate point on this other tip.
00:25:12.24 00:25:16.09 So these two planes, the object plane and the image plane,
00:25:16.10 00:25:17.22 are known as conjugate planes.
00:25:17.23 00:25:19.23 And the points within them,
00:25:19.24 00:25:22.27 that from which light comes and to which light goes
00:25:22.28 00:25:23.19 are conjugate points.
00:25:23.20 00:25:27.23 Now we can take other points on that same object,
00:25:27.24 00:25:29.23 and make the same sets of arguments
00:25:29.24 00:25:33.00 that rays passing through the middle of the lens don't bend,
00:25:33.01 00:25:35.00 rays that pass through the focus come out parallel.
00:25:35.01 00:25:39.03 And we can identify the other part, the other n of this object,
00:25:39.04 00:25:41.07 as well as each point in between.
00:25:41.08 00:25:46.04 We've used drawing essentially to
00:25:46.05 00:25:47.21 figure out where things are to go.
00:25:47.22 00:25:49.26 But this drawing is a shortcut
00:25:49.27 00:25:52.00 for some relatively simple math
00:25:52.01 00:25:53.28 which can also be used to
00:25:53.29 00:25:58.14 calculate where an object, and image are.
00:25:58.15 00:26:02.15 So the two equations that are worth remembering,
00:26:02.16 00:26:03.24 one is the thin lens equation,
00:26:03.25 00:26:08.11 which relates the distances from the object to the lens,
00:26:08.12 00:26:10.17 and that's denoted so,
00:26:10.18 00:26:14.03 and the the distance from the lens to the image,
00:26:14.04 00:26:15.17 that's denoted si.
00:26:15.18 00:26:20.10 Those two quantities are related to f,
00:26:20.11 00:26:23.03 the focal length, by this thin lens equation.
00:26:23.04 00:26:28.06 So that will tell you for a single positive thin lens,
00:26:28.07 00:26:31.15 or for a negative lens, where does the image show up.
00:26:31.16 00:26:34.03 The second equation is magnification,
00:26:34.04 00:26:36.12 often times, especially microscopy,
00:26:36.13 00:26:38.08 we want to know how big something is,
00:26:38.09 00:26:40.03 or we want to make it certain size,
00:26:40.04 00:26:42.24 we want to increase its size so we can see detail.
00:26:42.25 00:26:46.26 The magnification is, by definition,
00:26:46.27 00:26:48.00 the transverse magnification,
00:26:48.01 00:26:52.14 is the ratio of the heights of the objects and an image.
00:26:52.15 00:26:54.27 And those turns out are related to
00:26:54.28 00:26:58.02 the distances of the object to the lens
00:26:58.03 00:26:59.10 and the image to the lens.
00:26:59.11 00:27:01.21 I want to point out one other thing.
00:27:01.22 00:27:09.16 And that is when the object is in place, the focal length is,
00:27:09.17 00:27:14.02 so we don't, we are not placing the object on the focal plane.
00:27:14.03 00:27:15.27 So when we say something is in focus,
00:27:15.28 00:27:18.27 we don't necessarily, we don't always mean that
00:27:18.28 00:27:21.03 the object is in the focal plane.
00:27:21.04 00:27:23.13 We simply mean that we are getting an image
00:27:23.14 00:27:26.10 which is good quality.
00:27:26.11 00:27:29.10 So focus, that distance f,
00:27:29.11 00:27:31.25 isn't the place where you always put the object.
00:27:31.26 00:27:35.10 We'll talk about the case where you can put an object there,
00:27:35.11 00:27:37.25 but then you need another lens in order to form the image.
00:27:37.26 00:27:41.27 So we'll do another quick demonstration
00:27:41.28 00:27:44.24 about how to think about lens
00:27:44.25 00:27:47.17 forming images and a couple of examples.
00:27:47.18 00:27:51.01 For this demonstration,
00:27:51.02 00:27:53.13 we will look at the properties of positive lens,
00:27:53.14 00:27:55.20 and their ability to form images.
00:27:55.21 00:27:57.24 So I've got four things here.
00:27:57.25 00:28:00.16 One is the same light source that I used before.
00:28:00.17 00:28:05.13 It's connected by a fiber optic cable to a collimator.
00:28:05.14 00:28:08.18 And a collimator is simply a single lens
00:28:08.19 00:28:11.19 that takes the light that is emanating
00:28:11.20 00:28:16.27 from this fiber and creates a parallel, collimated ray.
00:28:16.28 00:28:21.18 So much like the diagrams in which rays are passing parallel
00:28:21.19 00:28:25.13 will be converged to a focal point by a positive lens.
00:28:25.14 00:28:28.23 So we can test that out simply by taking a lens.
00:28:28.24 00:28:30.01 These are two lenses.
00:28:30.02 00:28:36.02 Take one of them and we move it in the path of the light.
00:28:36.03 00:28:42.25 What we'd expect to see is that some position pass the lens
00:28:42.26 00:28:45.23 there should be the spot of the tightest focus.
00:28:45.24 00:28:50.15 And we can identify that using a simple piece of paper
00:28:50.16 00:28:54.20 and moving that from the lens position
00:28:54.21 00:28:59.04 until we see the tightest spot.
00:28:59.05 00:29:00.27 And now we see it expand again,
00:29:00.28 00:29:04.01 and tights, and expands again.
00:29:04.02 00:29:08.17 This is often a simple way of figuring out what lens you have,
00:29:08.18 00:29:09.26 if you have a lens in drawer
00:29:09.27 00:29:11.20 and you want to know what's its focal length,
00:29:11.21 00:29:14.26 being able to take a light source, even an overhead light
00:29:14.27 00:29:19.02 and position it such that the overhead light is in focus,
00:29:19.03 00:29:22.13 we're finding the minimum spot and then
00:29:22.14 00:29:25.01 taking a ruler and measure what that is,
00:29:25.02 00:29:28.28 you can get an estimate of the focal length of the lens.
00:29:28.29 00:29:33.16 Now just converging the rays to a focus is a good start,
00:29:33.17 00:29:35.13 but really we want to converge rays
00:29:35.14 00:29:38.20 to a focus from an object of interest,
00:29:38.21 00:29:39.19 so from a sample.
00:29:39.20 00:29:43.13 So let's add one more thing to this system.
00:29:43.14 00:29:46.07 And that is a tiny little cross.
00:29:46.08 00:29:52.27 So this is an opaque surface of glass that has a small,
00:29:52.28 00:29:57.04 thin cross that allows light through.
00:29:57.05 00:30:05.18 If we put his object at the focus of the lens,
00:30:05.19 00:30:08.13 it's being illuminated by this light,
00:30:08.14 00:30:10.08 but now at the focus of one lens
00:30:10.09 00:30:13.15 those parallel rays that are coming from
00:30:13.16 00:30:17.18 different spots on that cross
00:30:17.19 00:30:19.28 are coming through this lens,
00:30:19.29 00:30:23.28 and if we look at where the light is,
00:30:23.29 00:30:28.21 we can see initially there is an nice sphere,
00:30:28.22 00:30:32.04 a nice circle, rather, of intensity,
00:30:32.05 00:30:34.09 and that circle of intensity is going
00:30:34.10 00:30:36.15 smaller and smaller and smaller.
00:30:36.16 00:30:40.16 And right where we find the smallest
00:30:40.17 00:30:44.02 circle of light from the focus of the lens,
00:30:44.03 00:30:47.23 we see the image of that cross.
00:30:47.24 00:30:52.23 The image of the cross, if you go above it, it blurs out,
00:30:52.24 00:30:54.16 if you go below it, it blurs out.
00:30:54.17 00:30:58.10 And it's interesting to know how uniformly illuminated this is.
00:30:58.11 00:31:01.03 You wouldn't know that if you look at that intensity that
00:31:01.04 00:31:04.20 this is a cross or rays from a cross.
00:31:04.21 00:31:09.25 It's only at the position of best focus where you see the cross.
00:31:09.26 00:31:15.03 Now we also know that you can put lenses together and
00:31:15.04 00:31:20.14 increase the magnification or change the location of images.
00:31:20.15 00:31:23.24 So what if we add a second lens to that system?
00:31:23.25 00:31:27.00 So we've taken an object, we've created an image,
00:31:27.01 00:31:29.14 if we add another lens,
00:31:29.15 00:31:33.05 we should be able to use this as the object,
00:31:33.06 00:31:34.20 and created an image.
00:31:34.21 00:31:41.15 so if we look at the wall, and if we adjust the position of this lens,
00:31:41.16 00:31:45.17 we've now created an imaging system
00:31:45.18 00:31:49.12 where I have a two lens system.
00:31:49.13 00:31:56.09 I've taken one step to change the size of my cross,
00:31:56.10 00:32:00.06 this is actually demagnifying a little bit.
00:32:00.07 00:32:03.21 And this is magnifying.
00:32:03.22 00:32:09.24 So the size of this cross is substantially smaller than that one.
00:32:09.25 00:32:12.08 and based on our Lensmaker's equation,
00:32:12.09 00:32:17.05 we should be able to determine based on the focal length of a lens
00:32:17.06 00:32:20.02 the separation between the object and the image,
00:32:20.03 00:32:22.19 we should be able to calculate that,
00:32:22.20 00:32:25.25 and similarly we should be able to get the magnification out of those
00:32:25.26 00:32:31.20 by the ratio of the distances.
00:32:31.21 00:32:36.29 OK. So hopefully now you believe that when you have a single lens,
00:32:37.00 00:32:42.06 you are able to control the angles which light is propagating.
00:32:42.07 00:32:46.01 And you are able to form an image from an object.
00:32:46.02 00:32:49.01 Now let's take a few harder cases.
00:32:49.02 00:32:52.23 So one is in which we move an object into places
00:32:52.24 00:32:55.03 that don't create a real image.
00:32:55.04 00:32:59.18 So call images where the light actually converges
00:32:59.19 00:33:01.18 and creates an intensity pattern,
00:33:01.19 00:33:02.28 we call that a real image.
00:33:02.29 00:33:04.16 And those are the kind of images that
00:33:04.17 00:33:07.12 we put onto CMOS cameras,
00:33:07.13 00:33:09.03 those are the kind of things we record.
00:33:09.04 00:33:11.08 Because we want to be able to know
00:33:11.09 00:33:12.27 what that intensity distribution is,
00:33:12.28 00:33:15.15 and real images are required for that.
00:33:15.16 00:33:18.22 But in some situations, for example, in eyepieces,
00:33:18.23 00:33:21.25 we want to create virtual images,
00:33:21.26 00:33:24.27 and the example of creating a virtual image
00:33:24.28 00:33:26.04 shown in the lower figure,
00:33:26.05 00:33:30.00 and the way you can accomplish this with a positive lens
00:33:30.01 00:33:34.14 is to move the object inside the focal distance.
00:33:34.15 00:33:38.03 So for your so to be smaller than your focal distance.
00:33:38.04 00:33:41.14 And what that means is that the actual rays
00:33:41.15 00:33:43.14 that coming from this object
00:33:43.15 00:33:46.29 are going to diverge coming out the lens.
00:33:47.00 00:33:49.15 But if you trace those rays back,
00:33:49.16 00:33:54.11 the object, or the image that appears to be coming from,
00:33:54.12 00:33:56.03 if we didn't have the lens there at all,
00:33:56.04 00:34:00.21 it appears that the light is coming from a virtual image.
00:34:00.22 00:34:02.20 So that's the concept of a virtual image.
00:34:02.21 00:34:06.26 Your object is real, but you're creating a virtual image
00:34:06.27 00:34:08.11 that someone looking at this
00:34:08.12 00:34:10.26 didn't know there was a lens there,
00:34:10.27 00:34:13.21 they would think that it's coming from that virtual image.
00:34:13.22 00:34:16.16 So the same can be done with negative lenses.
00:34:16.17 00:34:20.17 You have an object and you create a virtual image
00:34:20.18 00:34:24.21 because the negative lens wherever you place the objective
00:34:24.22 00:34:28.29 is going to diverge the rays and again tracing those rays back
00:34:29.00 00:34:32.08 where they appear to come from is the virtual image.
00:34:32.09 00:34:38.15 And you can conversely use a negative lens to take rays
00:34:38.16 00:34:42.16 that are converging and move the position of image formation.
00:34:42.17 00:34:45.06 So that it creates a virtual object.
00:34:45.07 00:34:47.20 That's shown in the lower picture.
00:34:47.21 00:34:54.18 So with a basic understanding of waves, of rays,
00:34:54.19 00:34:57.04 and how they move through surfaces,
00:34:57.05 00:34:59.07 and how you can shape surfaces
00:34:59.08 00:35:02.01 in such ways to control where the rays go,
00:35:02.02 00:35:05.09 you can start to assemble combinations of lenses.
00:35:05.10 00:35:09.05 So that defined curvatures of multiple lenses
00:35:09.06 00:35:12.25 can be used to take light from an object
00:35:12.26 00:35:18.27 and reform it into an image through a set of lenses that eventually
00:35:18.28 00:35:21.09 when you add all of the special features
00:35:21.10 00:35:23.00 that we need for light microscopy
00:35:23.01 00:35:25.16 become the modern research microscope.
00:35:25.17 00:35:28.23 And that's the objective here is to introduce you
00:35:28.24 00:35:32.25 to the very fundamentals of lights and image formation
00:35:32.26 00:35:34.17 so that you can begin to understand
00:35:34.18 00:35:37.26 what exactly the microscope is doing.
00:35:37.27 00:35:41.06 So just to review, we talked about the properties of light,
00:35:41.07 00:35:44.29 its wave nature, and the different properties
00:35:45.00 00:35:48.26 that allow us to work with it,
00:35:48.27 00:35:51.03 and for it to generate contrast in samples.
00:35:51.04 00:35:52.11 We talked about light-matter interaction,
00:35:52.12 00:35:56.25 refraction and reflection, most importantly,
00:35:56.26 00:36:01.07 and how with refracted lenses you can control the curvature,
00:36:01.08 00:36:02.15 the shape of these lenses,
00:36:02.16 00:36:06.16 and define where an object and an image will be.
00:36:06.17 00:36:08.26 And finally this image formation
00:36:08.27 00:36:12.23 can be achieved by controlling those positions
00:36:12.24 00:36:14.28 and assembling sets of lenses
00:36:14.29 00:36:18.22 that give the desired magnification with the desired resolution.
00:36:18.23 00:36:47.02 So that's our first step towards understanding what's inside.

This Talk
Audience:
  • Student
  • Educators of Adv. Undergrad / Grad
  • Researcher
  • Educators
Recorded: March 2012
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Talk Overview

Light microscopes use lenses. The basic properties of light, how light interacts with matter, the principles behind refractive lenses and how lenses form (magnified) images will be introduced in this talk.

Questions

  1. A light ray travels through water and hits a layer of glass at a right angle. What fraction of the light ray will be reflected at this interface (assume a refractive index of 1.33 for water and 1.52 for glass)?
    1. 4%
    2. 0.9%
    3. 0.45%
    4. 0.1%
  2. A light ray traveling through air hits a layer of glass at an angle of 45 degrees from the normal. At what angle from the normal will the light ray travel through the glass?
    1. 45 degrees
    2. 39 degrees
    3. 34 degrees
    4. 29 degrees
  3. Which property of light remains the same when a light ray moves from vacuum to water?
    1. Velocity
    2. Frequency
    3. Wavelength
  4. Given a microscope equipped with infinity optics, including a tube lens with a focal length of 25 mm and a 100x objective, what is the front focal length of the objective lens?
    1. 0.25 mm
    2. 25 mm
    3. 0.25 m
    4. 2.5 m

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