 Okay, let's we start with this conference that is very, very basic, Miguel will continue with this context and you will see that we will repeat again and again because this is very important you to know about these lectures because this is what you will see in the lab. This is the basis of all the lectures and so on then as I say you a microscope is built with different lengths but not single length. We will derive the theory of microscope using single lengths but in real world the microscope objective is a complex sex of lengths but the theory of a single length apply for this. You only need to know some basic complex lengths make a equation image formation with different lengths and then you can apply this to the microscope objective and also we will have a lecture about a microscope objective tomorrow and about resolution but to understand what is inside a microscope we need to know this complete theory we need to know about the properties of light and how the light interact with matter this will answer some of the question you gave before. Also about refraction and reflection refractive lengths and finally about image formation. Let's we start with very very simple theory about the electromagnetic specter we know that the electromagnetic specter or the human eyes is only able to capture very very small region of this spectrum here in the visible for 400 to 700 nanometers different animals have different vision but also we are showing here different scales to compare to compare and with the light and also with microscopy but also it's very important when we use microscopy for example fluorescent microscopy or optical tweezers to know about the absorption of our skin for many medical application using lasers and light this is very important because for example we have here in this figure we can see how different components of the skin absorb for example water in the UV region of the spectrum also in the infrared different components hemoglobin melanin photofrein and so on and this make that in this region between 700 and 1 micron we have the optical window for the for humans a skin due to that normally we use for manipulating cells for a depilation laser depilation we use 900 nanometers because there is less interaction with the with the skin and the damage will be decreased also the properties of light because we will derive also here in my in my in my course and also in Miguel course about the rate theory but also about the wave theory because as I say you before in microscopy mainly in image formation for deriving very very simple equation that we use right optics but for the deriving there the for example the point spread function we need to know about wave optics for image formation for aberrations and so on due to that it's very important to know the main or to remember you because I know this is very basic maybe for many people here but maybe for others no and we have to remember this the the line is an oscillation not physical oscillation is oscillation of the electric field and magnetic field in space a sinusoidal variation this wave has amplitude this is the amplitude of the electric field wave length the wave length is the distance between to minimum or to maximum we also have frequency this is the inverse of the wave lengths speed of light phase depending on the this oscillation when it's starting in the space and also we have polarization intensity the the for example the laser the helium and laser are mainly polarized in some direction for example it's very important for a polarization microscopy to know about this this concept but there is a very very basic equation that relay these parameters wave planes frequency and the speed of light this equation and also the the electric field is related with the intensity through this relation our eyes is not are not able to detect this very very fast variation 10 to 14 hertz only reacts and detectors of course reacts to the square of this field and due to that we will use mainly the intensity of light as a square of the electric field but less we show you an example that this also very common in many application in medical application and also in biological application you must know about very important parameters and of course when you look at the paper this is the the main parameters reported there let's we look at very very simple laser pointing okay we say wavelength c-handed 35 nanometers with a power 2 milliwatts a spot area this spot area onto the sample a of course you can concentrate with the length and you will take this spot area you increase or reduce the power density but the less we take this a small a a millimeter spot of course the speed of light is also necessary here with this area and then the electric constant the electric constant and with this we can calculate for example the intensity or the irradiance some people say irradiance some people say intensity I say irradiance because intensity is also used taking into account for the angle and irradiance is only when you take into account the the area then maybe confusing but it's a question of definition the electric field using this and the equation I show you before you can calculate can calculate the electric field of the of the laser that is very very very very high intensity the spot area for for example and the speed of light that mainly we were used in the last equation for calculating this okay also let's we speak about the speed of life in in vacuum in air we know that the speed of life as this quantity that I show before but when the light meet a medium the the speed is reduced and the the light change the wavelength not the frequency the the wavelength and the relation between these two speed of light in the air and the medium is what we call refractive index and is this is very important parameter that we will use in microscopy also is very important how we will select the materials for length and so on using this equation of course but also is very important in in microscopy to start off with the definition of ray optics for defining the image formation length maker equation and so on as I say you after that wave optics but let's we look at the relation between right and wave optics it's only a representation we can when we have a wave when we have a wave if we look at the points of the which has the same phase in in the space and time we call this the way from in this case we have a plane with way from this is for example for a collimate beam we have plane wave but for a point source is radiating we have a spherical wave and we have a spherical wave from as the phase of the same phase if we represent this oscillation by this plane and the direction of propagation perpendicular to these planes we will have a right right there and we can represent this wave by also by a right by taking into account this this consensus also we know that the point in vector where the energy is going is in this direction perpendicular to the to the wave forms then this is only a simplification to better understanding of the theory of the ray optics and wave optics but also it's very important lie matter interaction refraction and reflection the snail law because what we can do for deriving the the the length maker equation and what happens for total internal reflection all the process in microscopy when we go from one media to another media with different refractive index is to use the snail law what says the snail law okay the snail law first the first point is that the law of reflection states that the angle of incident is equal to the angle of reflection as we can see here and the angles are measured respect to this perpendicular plane this is the angle of instance incident and this is the angle of refraction and here will be the angle of reflection this is the first state of the snail law but the second step of the snail law is that this the relation the relation between between this angle and this angle is through the refractive index of different media okay the scene of of the transmitted angle times the refractive index of the glass is equal to the scene of of the incident angles angles times the refractive index of the air of if there is another medium then following this law you can account for the direction of the propagation of the of the rays but this is the law only take into account the direction qualitative description for quantitative description of the amount of light going there reflected or whatever you want is the Fresnel equation and there are different Fresnel equation but i will concentrate only in the Fresnel equation for normal incidents because as you increase the the angle this is the reflection of light when we take into account normal incidents and the transmittance of the light as we know a small piece of a microscope slide you have normal incidents a four percent of the air glass will be reflected in each surface but if we can change this proportion we change the angle and there is an account for that in the Fresnel equation you can look at this but for now with this is enough also refractive lenses and focusing and lens maker equation is very very important in microscopy and this is the lens maker equation normally we build a lens using two two surface and with this two surface that has different radius of curvature and also here account for the for the refractive index medium of the medium use here for the for the lens and the distance here between the top of this surface but normally we use a definition called as a length thin lens in which this is zero or almost zero it goes very very very well for some definition in microscopy and in optics and then we obtain this equation which is a very very good relation very good approximation between the focal length of the lens the refractive index of the medium and the radius of curvature of this lens but we can have different kind of lens depending on the surface we are using there for example we can have a converging lens positive lens in which we can focus the light but we can also have divergent lens if we use two concave surface or meniscus is a plane and concave surface of this kind of menisco and every kind of length keep this in mind because when you build an objective what you use is this a combination of length also for a chromatic and spherical aberration you use a combination of lengths and this is very very important only to keep in mind but also I say you that wave optics is very important let's we ask is the focus really a point when we focus a lie is really a point the question is no why not okay because the lie have a wavelength and it's not a right and we will have diffraction of course that is related with the limit of diffraction in microscopy and this is what we will have in the focal point of the lens this is the point spread function we have there some distribution of the intensity I see Miguel also will be speaking about about this distribution of the intensity there that normally is I read this okay I read this some minimum and maximum this is the the idea this and this is called it the point spread function and of course we will see in the lab also the importance of this and in each lecture we will be remembering them because this is related with the resolution of course you have a point there you can resolve any component in the cell but it's not it's not possible you have a limit due to the diffraction of light then there are also I will only mention about this Miguel will derive with a question very precise in microscopy the main aberration are a chromatic aberration that are related with the with the fact that different colors has different speed in a medium and different refractive index okay then they will be focused in different place the red light will be focused there and the blue light before and there we have a distribution of colors how to correct that okay using meniscus we will see that but also we have a spherical aberration that as I say you any surface is not the perfect focusing element and then in any case we have aberration how we can correct this okay for example even using monochromatic light we have a spherical aberration this light will be focused in different place this is what I say about single lens when we started they started using microscopy was impossible to have good image because we have different focusing the rise coming far away from the center will be focused far away and the light coming here they will be in different place there are some techniques for correcting this for example correction colors I will show you right now about this but let's we continue with ray of this and let's we explain about three important law for image formation I will repeat it many times because very important the first law state that any right that enters parallel parallel to the axis to the optical axis of the lanes for one side process towards the focal point of the other side this is the focal point towards the the focal point the second law states that any ray that arrives at the lanes after passing through the focal point through the focal point this is the right through the focal point f focal distance will be comes out parallel to the axis on the other side this is the right and the third law any ray that path through the center of the lens will not change it is the ratio oh if you have thin length of course change but as this right change but again they are parallel and you can consider it's a good approximation that they are not changed direction and then you can build the image here depending on where you add the object using these three laws very very simple not only the image also the size of the image and the magnification of the image and this that is also called thin length equation is very important and you will test in the lab with a rule you will test there this is the object distance this is where you put the object far away from the length you measure there this distance and the this is the distance where the image will be created this is what you need to know and the focal length of the of the length you know that if not you can look there and well you measure with a rule and you substitute here and you get where the image will be created which is very important because there you will put your ccd camera for example for imaging we will do that in the lab but also the magnification is related with this distance the magnification is related is the ratio between these two distance and also the height of the object is related with magnification but let's let's we think about this is what you were asking me when you look with a single lens very close to the eyes what you see is this you see there a right the image because the image is between the lens and the focal length you have you to look at virtual image due to that you you can see the the right image but in this in the other case you look at the real image as inverted image in the other case because the image was far away but let we look at image formation this is the fair law parallel beam of light will focus the light in the focal lens here this is for the first law but for the divergent lens the parallel beam of light will diverges and this is also very useful as I say you I will repeat this many times again fairs to unfair law of a image formation okay let's we follow this there are many many videos in internet showing this I encourage you to look at this and check this every day and then Google practice in the lab all this law but after we are in complete knowledge of this we also of course as I say you the snail law for for the derivation of this the snail law that I show you before is very important but what I will do now is to to add the object in different place even at the final of this of this video I will show you another video and you will see is a kind of video that is in internet that you can play there putting the image in different place because when you put the image in this different place I say you the three rules okay but now we will put the object far away for example from this focal point we put the object here the first law again right parallel right to the focus okay now we apply the second law the second law say we can use this focus but as we use this focus before we can use this focus like coming from the object passing through the focus will be parallel okay and we have now a point here we have the tip of the image here but we can also use the third law that says right coming up will be without any change and then we can build the image there and we also account for the size of this image but we did using the and is of course real image but inverted you can do also using the length maker equation and you will account for this size of the image and also for the for the magnification of the image of course let's we add the image in between the focal length and the length now right parallel right through the focus okay first law now the second law let's we use this because we had used this before then right coming from the focus right coming from the focus will be parallel okay right coming from the focus will be parallel they are diverging okay and the third law but we don't need the third but we can use we can decide here okay the third law said okay also diverging if we continue this slide back and we get all together there we have where the image will be created but this image you cannot see you look at this image and you look at there is an object it's a virtual image it's not real image and it's also amplified image this is magnified image this is what also we have in when we use also diverging diverging lengths okay this is also what happened in our eyes in our iris when we have different uh beings coming from the from the object using this three law we can construct can build the image in our eyes then this is very very important concept that we have to keep in mind and I think that uh with that and this video will be uh all for uh let's we look at this I will explain what is uh telling there but it's also very interesting because he will show here uh how we can create the image in different place there are some some internet some of this kind of this video that I encourage you to use this every day and then when we go to the lab during this day you will be able to understand what is happening there okay this is what happened with the person having a correction in our eyes okay if the light is focusing before before the retina we add a diverging lengths there and the opposite when we have another kind of a correction there if the light is focusing there after our retina we add a converging lengths but now uh now he's explaining here uh what I say before what I say before the important or the basis concepts of uh of reflection and image formation using lengths and now we will start with very very nice very nice uh application on what I say uh before okay using converging and diverging lengths here he's explaining here what's happening to the light and very nice comparison with a a group of musician military musician when they meet an obstacle this is what happened to the light when the light reach this uh medium with higher refractive index and look at this to understand even using waveforms the the part of this band coming ahead they will be the first slowing down the velocity then they will be here slowing down the velocity but this will be going more faster then what happened to the way from the way from change then due to that we have a refraction there in this direction this is playing very well what happened in uh in a medium with high refractive index and now let's we look at this very interesting application about what I say before about the the three laws look at this for example the object at 2f we will do that in the lab we will soon we will see that when the object is playing twice the focal length of the lens we will have an image exactly twice the focal length of the length with the same size by the way we will have very nice image of the face of alber Einstein and we will we will look there and you will play with this and you will measure with the rule you will see when the image will be very clear he's explaining now about the first law lie parallel lie through the focus okay lie through the focus lie parallel and we have the tip of the image and the third law only only will confirm that this is a tip of the image and as he said we have an inverted and an image without any magnification if you use the lens maker equation and you calculate you will see that you take this distance you put in the question you take the focal distance and you will see that the image will be without any magnification exactly at 2f okay but what happened is we put the image in between the lens the focal length and the length okay the first right first right coming parallel go through the focus the second right coming from the focus go parallel and we don't need the third right okay okay but the third right doesn't coincide also then we have again diverging the continuation back here and we have a virtual and also magnify image of the object there this is what we have when we have a lens very close to the eyes very close to the eyes and we look at the book we can see the image not inverted this is what I show in the book there single lens and this is very interesting see what happened when you move there the image get virtual and then back you create the image this is a confirmation or what we said before and now okay he will show us a divergent lens divergent lens again parallel beam of light normally we use convergent lens but also it's possible to use divergent lens it's good to know about this when we use divergent lens right parallel right diverging through the focus again the second right again through the center no any deviation here we construct here from the focus parallel beam of right and we have this right and here no deviation if the if the right is passing through the center then we have an image here we have reduced image and virtual this is what happened see what how change the size of the image when we move there okay we have time Miguel please save me okay we have okay eight minutes maybe for question I am almost reaching the final of the lecture okay now okay that's all thank you for your attention let's we let's we take