Free Physics NEET Video Lectures for Wave Optics

00:00:33 [Music] [Applause] Welcome to the lecture module on optics. So far we have described propagation of light in terms of propagating rays or we described light in terms of ray optics. propagation of light and the various effects that we have studied so far in the earlier lectures in terms of ray optics. But there are several effects such as interference for example which is responsible for color of uh soap films. the colors that we see uh different colors in white light that we see of soap films or what is known as

00:01:26 defraction or u polarization. These are some of the effects which cannot be described by ray optics. And then we have to move on to wave optics. As I have discussed in the beginning of this uh course module that whenever there are certain areas which can be discussed by one approach whereas certain aspects can be discussed by another approach and so now we move on to wave optics. So in wave optics we will so here it is wave optics and uh let me first uh uh discuss uh the various topics that I'm going to uh

00:02:06 discuss in this course. So here so the various topics which we will see is first we will begin with hygen's principle reflection and refraction of plane waves using hygen's principle. Hygen's principle is the first time when light propagation was described in terms of waves. Then we move on to interference. First we will discuss a little bit about superposition of light waves and then describe the Young's interference experiment in detail. The Young's two-hole experiment or Young's double uh

00:02:47 slit experiment is will be described in detail. Then we will move on to defraction where we will describe single slit defraction. Defraction by a circular aperture and we will also discuss the resolving power of optical instruments and then finally we will come to the concept of polarization of light and uh we will discuss polarization by reflection. There are different ways of obtaining polarized light but in this course we will discuss polarization by reflection and the Brewster angle. So before we proceed we

00:03:29 will first discuss some historical milestones which led to the development of wave optics. So here are some of them which I have listed here. In 1621, Snell gave the Snell's law, Snell's law of refraction where we knew that BA it's an empirical relation based on experimental observations. Snell came out with the relation that sin I by sin R is equal to N_sub_2 by N1. This we have discussed in detail in the earlier uh lectures. And then in 19 in 1637 in 1637 the explanation of Snell's law was

00:04:15 provided because Snell's law was an empirical relation based on experimental observation. There was no theoretical support for that. However, in 1637, an explanation of Snell's law was given by Desakartis based on a corpuscular corpuscular model of light which was later established by Newton and now it is known as Newton's corpuscular theory. In 1678, Hygens put forward for the first time the wave theory of light. wave theory of light where the propagation of light is described in terms of propagating waves. However, as

00:04:58 we will see that Hygen could not answer certain questions such as what kind of waves are these and therefore the corpuscular theory prevailed even though Hygens put forward his wave theory in 1678. For about a century thereafter, the corpuscular theory prevailed only in 1801 when Young presented his interference experiment, the two-hole interference experiment which gave a convincing experimental evidence that light is a wave. Of course, subsequently in 1864, Maxwell put forward the theory of electromagnetic waves and then it was

00:05:44 known that light is an electromagnetic wave which was subsequently experimentally verified later. So these are some of the milestones to see and although the hygen's wave theory is no more used in optics but the development of wave theory this was the foundation for the development of wave theory that's why it's a historical milestone as an historical milestone we will first discuss the hygen's principle and hygen's theory of light propagation so first recall that we will discuss a

00:06:21 little bit about what we know about waves and wave propagation. So here what I have shown is recall that a plane wave can be expressed as s of xt the disturbance a wave is a propagating disturbance. So the s of xt can be represented as a cos kx minus omega t. This kx minus omega t is called the phase term. So this is the phase and this is the amplitude. A is the amplitude and kx minus omega t is the phase term where k is equal to 2 pi by lambda. lambda is the wavelength of the wave and omega is the angular frequency

00:07:03 which is equal to 2 pi into new. Omega here is the angular frequency equal to 2 pi * new where new is the frequency. At any instant t is equal to t1. The surface of constant phase. It's a plane wave. Why this is called as a plane wave? Because the surface of con constant phase which is called the wavefront. A plane wave is a propagating wave with plain wavefronts. Plain wavefronts. Wavefront is a surface of constant phase. Therefore at any instant t is equal to t1. The surface of constant phase is

00:07:48 obtained by putting this phase term is equal to constant. So kx minus omega t1 is equal to constant at an instant when t is equal to t1. Therefore this part is constant. So this implies kx is equal to constant or x is equal to constant because for the given wave k is equal to 2 pi by lambda is a constant and therefore x equal to constant represents surfaces of constant phase x equal to constant. If we plot here that x is equal to constant are planes which are perpendicular to the x-axis and that's

00:08:28 why it is a plane wave. So at t is equal to t_1 we have a plane which is here which is shown here is the surface of constant phase or the wavefront. The wavefront is a plane. Now at a later time so these are planes perpendicular to the x-axis what is shown here. At a later time t as t increases let's say at a t is equal to t1 + delta t x has to increase as t increases x has to increase if this term has to remain constant. So if we are tracking this wavefront then the wavefront is defined by this equal to a constant some

00:09:13 constant value and therefore if t increases x has to increase which means as t increases x increases for a given wavefront. In other words the wave will move in the positive x direction. So this where K is called the propagation constant or the phase constant because the phase constant multiplied by the distance traveled here would give the propagation phase. It is also at any given instant. So that is a plane wave. Plane wave propagating in the X direction. What about waves propagating in an arbitrary direction K. So let us

00:09:56 see waves propagating in an arbitrary direction K. So here I'm I have put waves propagating in an arbitrary direction K. That is K is here. So XYZ axis is shown. Such plane waves can be represented by S is equal to A cos K do R minus omega T. Now K is propagating in an arbitrary direction which means it will have three components. K is a vector with the three components kx ky kz and r. So r is the position vector which is also given by iixx j y + kz and k dot r therefore is equal to kxx k dot

00:10:45 r k y and kz. So k dot r is equal to kxx plus k y + kz. If this is a plane wave, this must be constant at a given time that will give us the wavefront which is a plane. So therefore that implies k dot r must be equal to a constant. So what is k dot r? k dot r is kxx plus k y + kz which is equal to constant. And we know that this is the equation of a plane. We know that the equation of a plane is a x + b y + cz is equal to constant represents a plane and therefore this represents a plane. K here k dot r is equal to constant. K

00:11:37 here is perpendicular to the planes. K dot r is equal to constant implies k is perpendicular to the planes. Its direction represents the direction of propagation of the wave. And the magnitude of this K vector is the same what we have discussed earlier as 2 pi by lambda. The magnitude of the propagation vector is 2 pi by lambda is the propagation constant. So K the point to note is the propagation vector K is perpendicular to the wavefront which is true even in the earlier case we did not show it as a

00:12:18 vector because K was along the X direction and the wave was propagating along the X direction but K in this case is also a vector but having only one component and K is perpendicular to the waveframe. So this is the representation of a plane wave propagating in an arbitrary direction. Now let us look at spherical waves. So we have seen plane waves propagating along a particular direction and plane waves propagating in an arbitrary direction. And now spherical waves. So what is a spherical wave? A spherical wave can be

00:12:58 represented in this fashion. As before, if we extend the definition of the wave, spherical wave must mean a wave with a wave front which is a sphere. So the wave fronts must be surface of sphere. And let us see a representation like this whether it represents surfaces of sphere is surfaces of spheres or not. So s of r is equal to a by r into cos k r minus omega t. Surface of constant phase at any given instant t is equal to t1 is k r is equal to constant. As before earlier we had k dot r and before that

00:13:41 we had kx. Now we have k r equal to constant because this part is constant here at a given instant. And this implies that r is a constant. R is equal to constant represents surface of a sphere of radius R. So schematically shown here that these are of course this is a cross-section in 2D but these are r is equal to constant represents a surface of uh a sphere and therefore spherical waves are represented by the phase term which is kr minus omega t. What about the r which is here? So we will see in a minute as t increases

00:14:25 therefore in this expression we see as t increases r has to increase so that the phase remains constant because we are tracking a particular wavefront. A particular wavefront is defined by the phase ph face phase here equal to a constant. And therefore as t increases r increases so that this remains constant for a given wave. And therefore the waves as t increases r increases which means the wave is expanding the spheres are expanding outwardly with the propagating time. This is typical of point sources. If I take a point source

00:15:07 here, it would give light. It would emit light a point source at the then it would emit light in all directions. The wave fronts are in the form of spheres expanding spheres. So that is represented by s of rt is equal to a by r into cos k r minus omega t. We come back to this r. Now this r in the denominator takes care of the decrease in intensity. We know that the intensity is equal to c² and that means a² by r² which is proportional to a² by r². And therefore we also know that the intensity decreases power or intensity decreases

00:15:54 inversely as r² that is it is proportional to 1x r² and therefore the amplitude must be proportional to 1x r that's why we have a r in the denominator here. So this is about the spherical wave with this we come to hygen's principle. Now with these uh basics we look at the Hygen's principle. Now how to propagate waves. So here is Hygen's principle. This not a a specific statement but it means the the the essentials of Hygen's principle essential aspects of Hygen's principle. All points on a

00:16:35 wavefront act like point sources that give out secondary wavelets which propagate outward with the speed of the wave. The wavefront at a later time deltat t is given by the surface tangent to these secondary wavelengths. We will come back to this statement. We will illustrate what does this mean and then we will come back to this statement and then we will understand it fully. So let us see let's consider propagation of plane waves using hegen's principle. So here propagation so we will come back to

00:17:16 this statement after a while. So propagation of plane waves using hegen's principle. So let me consider here. So keep so consider propagating plane wave. So here is the wavefront. So the plane waves are coming like this. So let me show two wave fronts. So plane waves at a later time. So plane waves are propagating like this. Now if this is the wavefront at t is equal to t_1 the wavefront plane wavefront which is propagating in a particular direction and therefore the k vector the propagation. So this is these arrows

00:17:58 represent the direction of k and this could be the x direction in that case the wave is represented by a cos kx minus omega t. So here is the propagating direction. So according to Hygen's principle every point on the wave act like source of secondary wavelets that is act like point sources of secondary wavelets. So what I'm showing here is point sources. So point sources of sec if this is a point source we know that this will give out spherical waves. So this will give out so spherical waves

00:18:43 like this. So each point source gives out spherical waves like this. So I'm drawing the spherical waves. And therefore at a time so let me bring the statement again. All points on the wavefront on a wavefront act like point sources that give out secondary wave. point sources which means sperical wavelets it will give out which propagate outward with the speed of the wave and that means in a time at a later time t is equal to t1 + delta t the spherical waves which are here would have moved so the radius of this

00:19:32 sphere here radius of this sphere would be v * delta t. So this will be equal to the radius the radius which I have shown here of these spheres at a later time delta t would be equal to v * delta t. And the statement says the wavefront at a later time deltat t is given by the surface tangent to these secondary wavelets. Which means if I draw a surface like this which is tangent to the secondary wavelets then this would represent the wavefront at the time t is equal to t1 + delta t. Please let me

00:20:19 repeat the wavefront is plain at t is equal to t1. According to Hegen's principle, every point on the wavefront here would represent would act like point sources and give out secondary wavelengths. The wavefront at a later time delta t that is t1 + delta t is given by the tangent to these secondary wavelets. So you have a tangent which is here and they will be propagating outward. So the wavefronts are propagating outward. We can see here that we could also draw a tangent here. Just uh for curiosity but that means the wavefront

00:21:06 at a later time could be on this side. But we know that the wave is propagating in this direction. And therefore, hygens conveniently said that there is no amplitude in any direction except in the direction of propagation. The amplitude is finite only here. So let me show this slightly bigger. So here is one of the point sources. That is one of the point sources on the wavelet. So here is the wave front on which we are. So this spherical wave is propagating outwards. But if the wave is propagating in this

00:21:47 direction, Hygens said he assumed he postulated that the amplitude would be finite only here that is which is at the point of the tangent and there is no amplitude anywhere else. This is of course Hegen's assumption there to avoid the issue of backward propagation in this case and therefore he said that the amplitude is finite only here in the direction of propagation and therefore the new repres wavefront will be represented by this. So this will here is the blue line which will represent the new wavefront at a

00:22:30 later time t1 + delta t. If you continue this at a later time t1 + 2 delta t then we have to draw spheres of radius equal to v * 2 * delta t. Or alternatively you could consider secondary point sources here. point sources on the second wavelet and draw again spheres like this in the spherical waves coming out of the point sources and then they are tangent to the tangent to these secondary wavelets would represent the wave the wavefront at a later time. So this would be the wavefront at a later time t is equal to

00:23:19 t_1 + 2 * delta t and so on. In other words, the this represents this explains the propagation of brain waves in the direction of k with time evolution of the wave with time. So we come back once more just to the statement that all points on a wavefront act like point sources that give out secondary wavelets which propagate outward with the speed of the wave. The wavefront at a later time deltat t is given by the surface tangent to these secondary wavelengths. I suppose it is now clear. So let me draw the uh let me put a

00:24:08 pre-drawn diagram the same diagram which I have pre-drawn so you can see here just for clarity. So this was the wavefront at t is equal to t1 at a later time t is equal to t1 + delta t. So this I picked up three points here. Of course, every point there acts like a point source, but I have just shown three points and spherical waves which are emanating from here. And we draw a tangent to all the wavelets which give us the wavefront at a later time delta t1 + delta t. And if you continue then at a later time t is equal to t1 + 2

00:24:51 delta t you get the wavefront here and in the direction of propagation. So the new wavefront at a later time delta t is the envelope tangent to all the secondary wavelets. This is an important statement which we will apply in the subsequent u propagation and the amplitude of the wave at the tangent only that is the assumption that u that was required for hygens to show that the wave is propagating only in the forward direction. Now let us look at propagation of a spherical wave. So propagation of a

00:25:30 spherical wave using hygen's principle. So as before, so let me take a sphere here. So approximately so this is the point source and which has given out a spherical wave front which is propagating outwards because light is emanated from here. It's a point source and we have just seen that it gives out spherical waves which can be represented as a by r into cos k r - omega t. So this is pro. Now let us apply hygen's principle according to hygen's principle. Let me use a different color

00:26:10 here. So we have point sources. we consider point sources on this and then these point sources give out secondary wavelets this so I'm showing the forward half because he has said the wave propagates the secondary wavelets outward in the forward direction because the K is in this direction and according to hygens the amplitude will be present only at the tangent so I have drawn here wavefront fronts wavelets. These are secondary wavelets. And the new wavefront will be a tangent a surface which will be tangent to all the

00:26:54 secondary wavelets to all the secondary wavelets and that would be again a sphere. So if this is a sphere then this will be a sphere at a later time t1 + delta t. So let me put the put a pre-drawn diagram which will make it uh more clear. So here is the spherical wave. So the spherical wave at t is equal to t1 is here and we have point sources here. So I have considered I have shown here and the radius the radius here if we it is at a later time delta t the radius of these spheres here will be equal to v

00:27:37 into delta t where v is the speed of the wave in the medium. So that is how the spherical waves are propagating outward. And the statement again that the new wavefront at a later time is the envelope which is tangent to all the secondary wavelets. So this is I have drawn them by hand and here is a diagram we can see which is drawn using a computer. So we can see that so this is at a time delta t and this is at a time 2 delta t and you have wavefront which is tangent to all the secondary wavelengths. So plane

00:28:18 wave propagation in this direction. So these are shown as dotted because they are not to be considered in this direction. So we have in the direction of k the amplitude of the wave is present only at the tangent. That is hygen's assumption. And therefore here we can see this is the original wave here spherical wave and at a later time delta t we have the new wave which is tangent to all the secondary wavelengths. All right. So propagation is fine. So this way we are able to or hygen was he was able to explain or

00:29:00 describe the propagation of plane waves spherical waves or in general propagation of light waves but do the this principle or do hygen's principle or do this way of propagation does it satisfy the law of reflection and the law of refraction because Snell's law was already known and therefore does it satisfy the law of reflection and refraction which were already known at that time. So let us see explain the laws of reflection and refraction using principle as explained by so here is a plane wave incident on a mirror. So what

00:29:45 is being shown is a beam of light which is incident here and these are plain wave fronts wave fronts here and incident on a mirror. Plane wave incident on a mirror. PQ is the surface of a mirror at a certain time t1. At a certain time t1 the wavefront has just reached here a let me call this is the wavefront at a time t1. Now this end of the wavefront will take some more time to reach the other end. So if this is delta t, if the time taken is deltat t, then this will be equal to v * delta t. The point a, this is the wavefront,

00:30:35 ab is the wavefront. The point A has already touched the mirror and therefore light does not propagate beyond the other side because this is a mirror. It's a reflector and therefore the secondary wavelets will start coming out in this direction. So the secondary wavelets will be emitted in this direction. So they will start propagating in this direction with increasing time. As this end approaches here, the wavefront which has already reached here creates secondary wavelets and they start propagating coming out in

00:31:15 this direction because this is a reflector. For example, by the time the wavefront the point B reaches here this end of the wavefront here I have I have taken two points on this wavefront. So here at approximately 1/3 the the separation is approximately 1/3 2/3 of the total distance and this point reaches here by the time the point B of the wavefront by the time the wavefront reaches here we see that this will reach here and as this propagates further this will start giving out secondary wavelets. So this starts giving out

00:31:55 secondary wavelets and by the time the wavefront reaches here this point has reached O2. O2 is another point which will start giving out secondary wavelets. So this is the secondary wavelet. So this keeps giving out secondary wavelets and finally when this end of the wavefront reaches here this has already given out secondary wavelets. This has given out secondary wavelength. So how much time what would be the radius? For example, this will take this is so each segment the time taken to travel this is delta t by 3

00:32:36 because deltat t is the total time taken from b to c for the light wave to travel from b to c. Therefore the time taken by the wavefront to travel here. So delta tx3 this time the time corresponding to this distance of propagation is also delta tx3 and this will also be because I have taken three sometimes you can take only one point midpoint or four points whatever any number of points can be taken so I've just taken three different points and therefore this radius here will be v into delta tx3 v

00:33:13 into delta tx3 will be the radius of the wavefront which is here. And this will be equal to V * 2 * V into 2 deltat T by 3. And this radius here will be equal to delta T is the time taken here. And therefore that will be equal to V into delta T. And therefore V into delta T is this distance. So the radius will be obviously larger. So we have according to Hygen's principle. So we have shown the wave fronts here of the secondary wavelets. These are the secondary wavelets propagating outward from the points which we have considered

00:34:03 according to Hygen's principle. The new wavefront. So the we see the statement that we have written that the new wavefront is given by so the new wavefront will be the new wavefront at a later time delta t is the envelope tangent to all the secondary wavelengths. So the envelope which is tangent to all the secondary wave. So here is the envelope. I'm drawing the envelope. The tangent to all the secondary waves is a straight line. So we can see that it is tangent here. It is tangent here and it is

00:34:43 tangent here. So this will be the wavefront of the reflected wave which is a plane which is a plain wave. Once this is plain wavefront we know that it will start propagating in this direction with plane waves like this. So plane waves which are traveling in this direction which are parallel to this as time progresses. So I will show a more clearer diagram here. So this is how I have shown you how to draw the plane wave front on refra reflection from a mirror. So let me show you a pre-drawn figure here. So we can see here that the

00:35:24 three points which I had taken here I have taken only three points. In the previous case I had taken four points just to illustrate that there are so many wavefronts and the tangent would give the tangent to all the wavefronts would represent the wavefront after reflection. So in this case here I have shown only three wavefronts here three points. So one end so the end point here end point midpoint and this so end point midpoint and so there are only three points which are shown here and you can

00:35:57 see the incident wave and the reflected wave. So BO3 from here to here B3 is equal to delta T * V. If delta T is the time for it to travel here, which is also equal to the radius O of this wavefront because when this was at B, the point has already touched O1 here. The other end of the wavefront is at 01. Therefore, it immediately starts giving out secondary wavelengths. And therefore this is equal to 01 H which is also equal to O1 F here because this is a sphere. So O1 H or O1 F. So by the time the incident wavefront

00:36:42 reaches from B to O3 the explanation is written here B to O3. The secondary wavelets from O1 reach H from O2 to the point K from O2 to the point K here and so on and the surface tangent to these wavelets give the reflected wave which is shown here which is a plane and therefore subsequently it will propagate as we have already illustrated. So this represents reflection by a mirror. But let us see whether this satisfies the law of reflection. So let me put a better figure now. So here so let's see

00:37:24 whether it satisfies the law of reflection. This is the incident wavefront. This is the reflected wave. So now we have seen here AB is the wavefront just before it touches here AB and this is the reflected wavefront FC. If this is the normal to the mirror and the beam is incident like this which means this represents the angle of incident I here then this will be I because this is 90° so this is this angle here is also I because the whole angle from here to here is 90 minus I therefore this must be I and this is I.

00:38:09 Similarly, if this is R, then this angle has to be R. So, this angle is 90 minus I here. And this angle is R for this triangle here because this is 90° and this angle is R. Therefore, the remaining angle here is 90 - R. 90 - R here. And therefore, this angle must be R. So that's how we have this equal to I and this equal to R and therefore in the triangle A B C triangle A B C sin I this angle is I therefore sin I is equal to BC that is the opposite BC divided by A C hypotenuse here which is equal to BC

00:38:57 is V into delta T the time the distance equal to V into delta T bc equal to V into delta T divide divided by AC. Similarly in the triangle A FC A FC where FC is the reflected wavefront sin R this angle sin R is equal to A F divided by AF divided by A which is equal to V into delta T by A. And therefore it simply means that sin I is equal to sin R or I is equal to R which is the law of reflection. So the law of reflection is satisfied by Hygen's construction and propagation using the Hygen's

00:39:45 principle. Now let us look at the law of refraction. So law of reflection it is satisfied. Now let us look at law of refraction. So here it is refraction at an interface between two transparent media. So as before so this time I'm not drawing because it's shown here. Incident wavefront is here is coming here and by the time this travels from here at this interface the secondary wavelets start coming out. So the secondary wavelets come out and when B reaches here the secondary wavelet reaches here.

00:40:25 Note that the refractive index are different N_sub_1 and N_sub_2. N_sub_2 is greater than N_sub_1. If N_sub_2 is greater than N_sub_1, we already know by Snell's law that the ray will bend towards the normal or the beam will bend towards the normal. So if it has to bend towards the normal then if n_sub_2 is greater than n_sub_1 v_sub_2 should be less than v_sub_1. If we do not assume v_sub_2 less than v_sub_1, this distance here a d will a d will be smaller compared to b c here only if we assume that v_sub_2 is smaller than

00:41:05 v_sub_1 because this distance a d is equal to v_sub_2 * delta t. Unless this distance is smaller, this wavefront will not bend towards this. And experimentally we already know that if there is an incident ray like this then it will bend towards the normal if the second medium is of higher refractive index. Therefore it is essential to assume that v_sub_2 is less than v_sub_1 and if we assume v_sub_2 is less than v_sub_1 then this travels a distance a d. And similarly these points will travel the corresponding distance and

00:41:44 the tangent to all the secondary wavelets. This this and this here shown is the wavefront of the refracted wave at this point. And subsequently if this is plain it will propagate as a plane wave. So wavefront in the second medium is tangent to all the secondary wavelets. And that is how the wave propagation refraction at an interface between two dialectrics is uh two media of refractive index n_sub_1 and n_sub_2 are described using the hygens principle. So I keep a more clearer picture of the same picture to show the

00:42:26 law of refraction here. So the law of refraction by Hygen's principle. So see this this was the incident wave and wavefront and then this is the refracted wave. So we can see as before in triangle A B C A B C here sin I here will be equal to BC by this. So BC by A C BC is V_sub_1 into delta T. Now we have two media. This is of refractive index n_sub_1 and velocity v_sub_1. Here it is n_sub_2 and v_sub_2. So v_sub_1 delta t by a c in triangle a d c this triangle in the second medium sin r this

00:43:06 angle sin r the refracted angle this angle is the same as this angle and therefore sin r will be equal to a d by a c which is v_sub_2 * delta t by a c that means sin i by sin r therefore will be equal to v_sub_1 by v_sub_2 which is equal to N_sub_2 by N1 by Snell's law because Snell has by Snell's law we know that sin I by sin R is equal to N_sub_2 by N1. So V_sub_1 by V_sub_2 is equal to N_sub_2 by N1. N_sub_2 is larger than N_sub_1 and therefore V_sub_2 is smaller than V_sub_1 if N_sub_2 is greater than

00:43:48 N_sub_1. So the velocity of light has to be smaller in this medium. Now, Hygen's principle successfully explained both the law of reflection and the law of refraction which were already known during his time. So that was the plus point. However, Hygen had some difficulty. He could not answer what type of waves are these because it was known also that these light waves can propagate through vacuum without any medium. Then what type of waves are these? And therefore the corpuscular theory prevailed because corpuscular

00:44:33 theory had an explanation for what type of waves are these. And therefore the heens theory although although put forward in 16 although put forward as early as 1637 it could not be accepted for more than a century until 1801 when Thomas Young put forward his famous experiment which is the double hole experiment or the double slit experiment to prove that to convincingly demonstrate that light is a wave. So we will discuss a little bit more on this. Now before we go to Thomas Young's experiment, we will

00:45:20 see the application of Hygen's principle to light passing through apertures. So let me illustrate light passing through an aperture with by using the hygens principle. So what I'm discussing now is C consider plane waves incident on an aperture. Aperture means a stop which with a certain opening. So here is a stop for example it could be a screen or it could be an opaque uh plate with an opening here. Plane waves are incident here. Plane waves are incident on this aperture. According to hygen principle

00:46:07 when the plane wave reaches here. So when it has reached here. So let me use the blue color. Here we have point sources. The further propagation is discussed using the secondary wavelets. The point sources which are here are blocked by the aperture. So there is a aperture which is here. So which is which blocks it's a finite it's a plate of finite thickness or some obstacle and the wavefront which is here start giving secondary wavelets. So they give out because we have to see how it will propagate across this across the

00:46:46 aperture. So this gives out secondary wavelets. So with the time these secondary wavelets will become larger and larger and the tangent to all these so they will further become more and more. So these each one of the secondary wavelet again acts as point sources and therefore these give out wavelets which are like this. And we know that the wavefront at a later time is given by a surface which is tangent. So let me use the black color to draw the tangent which is tangent to all the secondary wavelets. So it looks like

00:47:29 this. It is tangent to all the secondary wavelets. But what we have seen is the wavefront now has a curvature. wavefront has a curvature which means although originally it was propagating like this now it is the K vector or the propagation direction which is normal to the wavefront also has components in the in the direction which is away from the original direction here if you see this more carefully what it means is that at if I plot the wavefront At a later time it would further become like this. So what it means is the wave is

00:48:18 also propagating in the geometrical shadow of the aperture. What is this word? I have now introduced the word geometrical shadow. Geometrical shadow. Geometrical shadow. What it means is if the waves are incident like this they are propagating in this direction then because of the aperture there's a shadow and this wave should have come directly here as far as if I use the ray theory for example rectilinear propagation of light I should have seen light only coming here and whatever is the remaining part. So if I use a

00:49:09 different color here. So this portion here is the geometrical shadow of this aperture. There's an aperture here and there is a geometrical shadow which means as far as the geometry is concerned the straight rays or the straight lines would go here and here because it's a it's a plane wave which was incident here. But we see that according to Hygen's principle when we construct the wavefront the wavefront also propagates into the geometrical shadow. In other words, there is light

00:49:45 propagating into the geometrical shadow which as we will see later is nothing but defraction. That is the phenomena of defraction. And therefore, Hygen's principle was able to explain defraction that is light propagating into geometrical shadow of the apertures. I have some diagrams here which will illustrate it more clearly. So let me show you some diagrams here. Hygen secondary wavelets at an aperture. So here so this is drawn using a computer. So plane waves are incident here. There's an aperture here. So we have

00:50:24 considered different point sources here and then constructed the secondary wavelets which are spheres originating from the point sources. As you can see there are no point sources here on the other side because this is an aperture and therefore the surface tangent to all the secondary wavelets looks like this. It is somewhat plain here but it also has curvature in this direction which means the wave is also propagating into the geometrical shadow. The geometrical shadow would have been here. So this is

00:50:59 the region where the light should have come but light is also propagating into the geometrical shadow. If you reduce the aperture size, if we reduce, for example, this is the opaque screen. If we reduce the aperture size, then we see that it spreads more. It it was almost flat here and a little bit of curvature at the other ends. But now you see that the flat region becomes smaller. It more and more looks like a spher. It is more moving towards a spherical wave. And if I reduce the aperture further. So let's

00:51:39 reduce the aperture further. And we can see that if the aperture size is reduced, the hygens construction gives us wave fronts which are approaching a spherical wave. Incident wave is a plane wave. And if you reduce it to a very small hole, then we almost have spherical waves which are emanating from the holes. This is contrary to what is expected from the ray theory. So we see that the wavefront is becoming more and more spherical. These observations were made by many scientists and many researchers

00:52:19 at that time and they were getting convinced that it light must be a wave. But there was no concrete evidence. There were no experimental evidence in with regard to light. Although there were mechanical waves, ocean waves which were seen to exhibit this kind of behavior but there were no experiments which could prove that light is a wave. So a further observation here with the two holes I showed you in the last diagram there's one pinhole or one small aperture here giving out almost spherical wavelets and if we what would

00:53:06 happen if there are two holes hygen secondary wavelets from two holes in a screen. So if we draw spheres which are from the two holes then we observe observe that there are directions where so what is shown here solid line and dashed line. The dashed line represents wave fronts corresponding to troughs. If a sinosoidal wave propagates like this it has troughs and crests. The amplitude is minimum here and amplitude is maximum here. This corresponds to so the two points are pi difference in phase. The

00:53:50 phase difference between the maxima and the minima is pi. So what is shown here are troughs. So wavefront corresponding to trough and wavefront corresponding to crest. Which means if I put cos omega t cos kx minus omega t assume that this is the x direction then the phase front here corresponds to kx minus omega t equal to a constant. This represents kx minus omega t equal to a constant. The constants are different. If this is this constant is pi then this constant is 2 pi. That's the meaning of

00:54:29 crest and trough. So I have shown here the wave fronts corresponding to the minima and maxima. So correspondingly if we see the wave fronts here the dashed line here corresponds to troughs and solid line here solid curves correspond to crest. So if you plot these these spheres then there are directions where you see that the solid line meets solid line the dash line meets dash line solid line meets solid line dash line meets dash line and so on. Whereas there are directions where you see that if one when it when

00:55:10 the two intersection point of the wavefronts one is a solid and another is a dash line. here solid line dash line solid line dash line. So there are directions where the crest due to one overlaps with the trough due to the other. And there are directions along which the crest due to one that is one hole one one point corresponds to crest due to the other point. Which means these there must be directions where there are bright light coming that is the maxima and maxima coinciding and the minima and the maxima and minima

00:55:54 coinciding which means there would be no light. So the int what is expected here is an intensity variation if we keep a screen here. So Thomas Young gave the double hole experiment in 1801. First with sunlight from a small opening in the roof and then with sodium light and the wave nature of light was convincingly demonstrated for the first time by Young's experiment and of course subsequently he also explained the Newton's rings in 1802 by the wave theory. Now let me explain a little bit

00:56:39 as it apparently the Young's experiment was done. The first time when he saw sunlight coming from the roof. So this is sunlight coming from the roof. He placed an aperture here. He placed a plate which had two holes. Two small holes here. So two small holes. This is sunlight from the roof. Sunlight from the roof. Apparently these are the sequence of events which led to the Young's double hole experiment. And then he could see on a screen placed here in a dark room sunlight coming from a small aperture in the roof. And there

00:57:35 is a plate with the two small holes. And he could see a bright fringe here. That is a bright intensity in at the center here. And then he could see some colors. And then so what I'm showing here is the intensity variation. I'm plotting some intensity variation. We will discuss this in more detail. So what I have plotted is this is a screen on the screen that is on a let's say a cardboard sheet or something that if you plot the intensity he could see a bright intensity peak a bright peak at the

00:58:18 center here and then he saw some colors here and then there is uniform illumination far away from here. This is now very well understood why he saw such a and we will discuss this in greater detail in the next class in the next lecture. But this is what Young saw and then what he did so this is first sequence the in the then what he did was he used a spirit lamp so spirit lamp here. So there's a flame which is flame of the spirit lamb and then sprinkled he sprinkled naaccl that is salt na he sprinkled

00:59:02 naaccl onto the flame of the spirit lamp which gave the bright yellow color corresponding to bright yellow light corresponding to the sodium here. And now he placed an aperture with the two small holes very close by two small holes. And on the screen here he could see a large number of bright and dark intensity maxima and minimas. Intensity maximas and minimas due to the bright yellow color of sodium. So this is a spirit lamp on which he sprinkled uh salt and then he saw due to the bright yellow light he could see bright and

00:59:53 dark fringes here that is maximas and minimas on a screen placed here. So this as we will discuss in more detail in the next lecture is a convincing evidence that light is a wave. Thank you.