 I have this glass of water here and between me and the water there are no mirrors, there is no cause for reflection and yet if I show you the water from the underside and then I point my flashlight, my phone flashlight from this side you can see the surface of the water begins to shine that is in fact reflecting the light from my flashlight and creating an image of my flashlight on the other side on the upper side of the surface it looks like light is coming to you from somewhere here when actually my phone is below the surface of the water this is the phenomenon of reflection that is associated with mirrors but there are no mirrors here this is the case of water air and glass three materials that are completely transparent and transparent means that the light on the other side of the material is brought through the material to this side which means there is no chance for reflection whatever reflection does occur in a very small amount and a large proportion almost all the proportion of the light is transmitted through these materials then why are these transparent materials why is the surface of water behaving like a mirror when I point my light from underneath this is the phenomenon of total internal reflection which you all must have heard of plenty if you are studying for JLE then you have definitely heard of total internal reflection you know what it takes for total internal reflection to happen you need the light going from a denser medium to a rarer medium and you need the angle of incidence to be greater than a particular value which we call the critical angle now this critical angle can be determined from the refractive index of the denser medium with respect to the rarer medium if this value is new then the critical angle is given by the sign inverse of 1 by pin now in the case of the water the last experiment which I just showed you the light from my phone enters the water performing a regular refraction but then while traveling through the water it encounters the water air surface and when it hits the water air surface it becomes a ray of light traveling from a denser medium water to a rarer medium that is light now what happens to this ray is that it is hitting above the critical angle and therefore it reflects instead of refracting following the traditional reflection loss that the incidence angle is equal to the reflected angle but why does this happen you all know that above the critical angle psi by psi are equal to mu no longer has a solution the formula based explanation but what is actually happening inside the material which causes light to suddenly start reflecting this phenomenon of refraction and total external reflection were explained traditionally in two ways one of them was by Newton who assume that light consists of tiny particles that are attracted to different media in different amounts another explanation which one out in the end for a long period of time was by a scientist called Christiane Huygens this person assumed that light is a wave and if you observe these crest points of the wave it's a 3d wave such that from a source the crest points spread out in circular shapes as you go further the radius of the circle increases and the crest points approach planar shape this plane is called a planar wave front and the consequence of planar wave fronts is that when this wave front approaches when a planar wave front approaches the boundary between two material then this wave front continues to go undisturbed but the material the boundary points of the material will release their own little spherical waves now if the wave front is parallel to the boundary of the material all the spherical waves are released simultaneously and depending on the nature of the material the waves may either constructively interfere with the original wave on this side or this side and destructively interfere with the original wave on the opposite side if it constructively interferes on this side the wave passes through which is a transverse medium and if it destructively interferes here and constructively interferes here the wave reflects back which we call a reflective medium like in the case of metals now this is the case where the incident wave front is parallel to the surface separating the media if the incident wave front makes an angle with the surface separating the media now these points correspond to the crests of several waves that are one after the other side by side in space different crests reach the border of the media at different times which means these secondary waves the wavelets generated by the border points are now not going to be generated at the same time in fact this wave will generate first then this then this and so on and you can see the edges of the wavelets will form and inclined surface and depending on the speed of these waves compared to the speed of these waves and on the intensity of the different waves there will be some amount of refraction which is which means this line of crests will get over at a different angle or there might be some amount of reflection which means the line of crests is going to reverse and propagate in this direction now if this side is an optically denser medium and this side is an optically rarer medium the line of crests is going to bend away from the medium surface and propagate in that direction and what happens after a certain angle is that the newly generated waves the newly generated waves will not destructively interfere on the inside of the medium and constructively interfere on the outside of the medium in such a way that a pure reflection occurs and all the energy is kept in the same medium this is the wave phenomenon of coated internal reflection explained originally by Christiaan Dragons and developed upon by the great scientist Frejana so it is the effect of interference between the incoming wave and the wave produced by the particles on the boundary which causes refraction as well as total internal reflection so my question is just like light is a wave sound is also a wave light is an electromagnetic wave which is an oscillation of field the electric and magnetic field is inside a medium but some is a pressure wave it is the up and down of pressure over a mean value within air enclosed in a space if sound is a wave can we apply this theory to sound as well in other words if sound crosses the border between two media does the sound refract and if it crosses from a denser medium to a rarer medium is there a chance of total internal reflection and the answer to both of these questions is yes sound is a wave just like light and snails law is not something that is specific to light it is a general law that applies to all kinds of waves traveling in any medium not just light and sound but also water waves traveling on the surface of water the ripples that you see produced when you drop something in water those ripples will also follow snails law if you go far enough from the source of the ripple so that the ripples tend to become straight lines or clean waves as we call them so now sound also undergoes refraction sound also undergoes total internal reflection but there is one important thing to keep in mind number one what is the refractive index of a material when speaking about sound you see when talking about light we define the refractive index as the ratio of velocity of light in that medium to the velocity of light in vacuum unfortunately sound does not travel in vacuum so we can't apply this definition to sound directly but refractive index is also defined for refractive index for a pair of materials the ratio of speeds of light in these two materials basically the speed of light in vacuum gets cancelled out when you take the ratio of refractive indices and the refractive index for a pair of materials is simply the ratio of the speed of light in these two materials the same thing you can do for sound which gives us the refractive index in the sense of sound as being the ratio of speeds of sound between two materials but an important point to make here is about density when we talk about refraction we talk about light going from a rarer to denser medium or a denser to rarer medium now a rarer medium in the sense of light is a medium where the speed of light is higher and a denser medium is a medium where the speed of light is lower which means an acoustically denser medium to take the pattern of optically denser media we find acoustically denser mediums have a lower speed of sound but the conventional sense of density is that solids are denser than liquids which are denser than gases but if you look at the speed of sound travel it is higher in solids due to the height of the bulk modulus of solids and slightly lesser in liquids and much less in gases which means solids are less acoustically dense than liquids and liquids are much less acoustically dense than gases and gases are acoustically denser stop all this is the reverse progression as to what we think of when we speak of light so solids are very much optically dense liquids are slightly less optically dense and gases are least optically dense but the order of acoustic density is reverse this is an important thing to keep in mind while calculating matters regarding to sound waves. The reason why total internal reflection of sound is not so easily demonstrable as light is that you don't commonly find an interface between two media where on one side you have a acoustically very dense medium and on the other side you have a very acoustically rare media. You see densities of media usually tend to vary slowly and it is in these examples where we find a sort of continuous total internal reflection of sound. What do I mean by this? Take an example of the phenomenon of a mirage shape an object that is in front of you will send light rays will reflect light rays from the sun in such a way that the light rays initially head downwards then the density change in the layers of the air causes this light ray to bend away from the model because the air is being heated up by the ground the lower layers of air are rare which means the light is travelling from a denser medium above to a rarer medium below which bends it away from the normal until total internal reflection occurs and the light swings around upwards to our eyes. Our eyes retrace the path of the light as if it is a straight line and it looks to us like the object is coming from there and we automatically interpret it as a reflection of this object in some body of one when in fact there is no water their reflection is actually a total internal reflection or a curved total internal reflection from the layers of air that are closest to the ground. An important application of this kind of curved total internal reflection is in the detection of submarines by ship using sonar as well as sonar stands for sound elevation and reaching it generates sound pulses and then looks at the echo of these sound pulses from different objects by analyzing the input from different objects it imports a graph of which object is where depending on how long the echo has taken to reach from that object to the receiver. Now in a sea you know that water is very slightly compressible so as we go deeper under the surface of the sea the water at lower layers is much more compressed than the water at upper layers which means the density here is less and the density here is greater because of the compression of water at lower levels of the sea. Now if the density is greater that means the speed of sound here is less the speed of sound is less than it is here if the speed of sound is less that means this is a denser medium or this is a rarer medium with respect to sound this means that as a ship on the surface releases a signal from its sonar this signal travels down into an acoustically denser medium which means it bends towards the normal and it hits say a submarine at this level. Now on the surface of the submarine reflects the sound back what happens is it reflects it in all directions because the surface is not smooth it is rough suppose a film extending at this angle reflects it back in a direction that seems to be heading towards the ship. At this point this rise traveling from an optically denser an acoustically denser medium to an acoustically rarer medium which means it bends away from the normal and this curvature continues until it hits the critical angle for this pair of densities once it hits the critical angle it begins to reflect back and go deeper into the sea rather than hitting the ship. This means submarines can hide themselves and they do in fact hide themselves by ensuring the presence of a large number of films of the submarine which would send off the signal from the ship in such directions that total internal reflection of the returning song is accomplished at a certain depth of water below the surface. This will help us hide the submarine which is an important application an important military application of the total internal reflection of sound which is something we haven't been able to hear much about which is something we don't hear much about compared to how much we hear about the total internal reflection of light. Nevertheless it is very important and has real world applications.