in this video we're going to go over the law of reflection and the law of refraction so let's say if this line represents the boundary between two materials above we have air and let's say below is glass and this vertical line which is perpendicular to the surface it forms a 90° angle with the surface this is called the normal line and let's say if we have a light rate that is incident on this boundary the incident Ray is the ray that strikes the glass and this is called the reflected ray I got to make it equal so this angle between the incident Ray and the normal Line This is called the angle of incidence this angle between the normal line and the reflected ray that's the angle of reflection the law of reflection states that the angle of incidence is equal to the angle of reflection so if the angle of incidence is 30° the angle of reflection will also be 30° that's the law of reflection refraction is the process where light bends as it passes through the air glass boundary so this Ray represents the refracted Ray and this angle inside is the angle of refraction it's between the refracted Ray and the normal line so whenever light strikes the boundary between two materials it can reflect or it can refract and just remember refraction is the bending of light as it passes from one material to another now there's something called the index of refraction and it measures how much light bends as it passes from one material to another the index of refraction for air is about one the index of refraction for glass is roughly about 1.5 so notice that the light rate travels from a low end value to a high end value as light moves from a low index of refraction to a material with a high index of refraction the light rate is going to bend close to the normal line therefore the angle of refraction is going to be less than 30 because it's going to been closer to the normal line and we can calculate that angle using Snell's law of refraction the equation that we need is N1 sin Theta 1 is equal to N2 sin Theta 2 so let's say one is for air two is for the glass so N1 is 1 * s of 30 which equals N2 which is 1.5 time sin Theta 2 now it turns out that sin 30 is .5 so to solve for sin Theta 2 you need to divide by 1.5 so sin Theta 2 is05 divid 1.5 that's basically a third that's point 3 3 3 repeating now to find Theta 2 what you need to do is take the inverse sign of both sides Theta 2 is the inverse sign of 1/3 or 333 and make sure your calculator is in degree mode not in radiant mode because M was in radiant mode so the angle that I got is 19.45 which I'm going to say about 19.5 degrees so as you can see it's less than 30 so whenever light goes from a low end value to a highend value as it moves from one material to another the light rate is going to bend closer to the normal line now if light were to go from a material from with a high index of a fraction to a low index of refraction so let's say if we were to go backwards the light Ray would bend away from the normal line the angle will increase so as the index of refraction of a material increases the angle decreases meaning that the light Ray it gets it moves closer to the normal line now another thing that you may need to calculate is the speed of light in a material the speed of light in a vacuum or empty space is 3 * 10 8 m/s but when light travels let's say in water or in glass or in Diamond will the speed of light increase or decrease it turns out that light it decreases in speed when it moves in a different material light travels slower in water than in empty space because there's more molecules in water that it has to get through there's an equation that can help you to calculate the speed of light in the material it's V which is equal to C Over N so if you want to find the speed of light let's say in water it's going to be the speed of light in a vacuum which is 3 * 10 to / the index of a fraction of water which is about 1.33 so therefore the speed of light in water is about 2 26 * 10 8 m/s now the speed of light is not the only thing that changes the wavelength of light changes whenever light passes through a different material as the index of refraction increases the velocity of light decreases so as you can see light travel slower in water than in empty space Also the wavelength decreases as well so here's an equation that relates wavelength with the index of refraction wavelength 2 / wavelength 1 is equal to N1 over N2 the inversely related now let's say one is for air and two is for the new material so this is going to be wavelength 2 / wavelength one and the index of refraction of air is 1 over N2 so I'm going to multiply both sides by wavelength one so these are going to cancel so then you're going to get this equation wavelength 2 is equal to wavelength 1 / N2 in most textbooks this equation is going to look like this wavelength n is equal to wavelength KN / n this is the equation that you want to know as well as this one too you should add those two equations to um your list of equations or if you have a formul sheet so what this equation says the wavelength of light in a vacuum divided by the index of a fraction of a different material is equal to the wavelength of that material so let me give you an example problem let's say if the wavelength of light in a vacuum is 500 NM what is the wavelength of light in glass so all we have to do is use this equation the wavelength of light in a material is equal to the wavelength in a vacuum divided by the index of a fraction of that material so the wavelength of this light is naturally 500 NM but we want to find the wavelength in glass the index of a fraction of glass is about 1.5 so 500 ID 1.5 is about 333.33 and the speed of light will decrease however the frequency Will Remain the Same by the way the frequency of light you can calculate it using this equation C is the speed of light Lambda is the wavelength and F is the frequency some textbooks might use v as the frequency but I'm going to use f because in physics V represents velocity but in chemistry V V could be frequency now this equation is for a vacuum in a different material you might see this equation so V is just the velocity of light or the speed of light in a different material other than a vacuum and Lambda is the wavelength of light in that material so let's calculate the frequency using the information that we had in the last example so the speed of light in a vacuum is 3 * 10 8 the wavelength was 500 NM which is 500 x 109 M if you're going to plug in uh the wavelength data into the equation make sure you put it in meters because the speed of light is in meters per second so we can solve for F so it's 3 * 10 8 / 500 * 109 and F is 6 * 10 14 Hertz the unit Hertz is the same as 1 / seconds or S theus1 now let's calculate the frequency using this equation so the wavelength for that equation was 333.33 using this equation we found the frequency of the light in a vacuum or in air now we got to find the velocity or the speed of light in glass using this equation V is equal to c n so that's 3 * 10 8 / 1.5 3 ID 1.5 is 2 so this is 2 * 10 8 so we're going to plug in this value for V and Lambda and we're going to see if we're going to get the same answer 6 * 10 14 so 2 * 10 8 is equal to make sure you convert Lambda into meters so it's 3333 and just add 109 m 1 nanometer is 10- 9 m so let's solve for f so 2 * 10 8 / 3333 * 109 you should get the same answer so f is 6 * 10 14 Hertz so as you can see the frequency of light does not depend on n as light moves from let's say air to Glass the frequency Remains the Same the wavelength and the speed of light decreases but frequency is constant now there's some other things that we need to go over and that is the difference between diffuse reflection and specular reflection diffuse reflection occurs on a rough surface let's say like a a polished wooden table and specular reflection occurs on a smooth surface like a mirror in theuse reflection light is scattered along the rough surface and so it's going to bounce off in different angles and so that's why you won't see your image clearly if you have a polished table you can somewhat see your image but not very clear so in such a situation diffuse reflection is occurring now in the case of specular reflection you can clearly see your image as in a case of a mirror because the surface is smooth light is not scattered at that surface it reflects in the same direction and so make sure you understand the difference between diffuse reflection and specular reflection because sometimes you might be tested on this concept now let's work on a few practice problems so let's say this is the first mirror and we have another mirror I'm going to call this M1 M2 and in addition we have a light Ray that strikes the mirror at a 30° angle and then this light Ray it bounces off and Strikes this mirror and you want to find the angle at which the light Ray leaves the second mirror so what is the angle Theta and let's say that the angle between the two mirrors is 110° feel free to pause the video and solve the problem and then unpause it when you're ready to see the solution so what's the first thing that we need to do to solve this problem well let's find this angle let's draw the normal line which is perpendicular to the surface and so here we have another normal line so if this angle is 30 this angle must be 60 it's complimentary they have to add up to 90 and according to the law of reflection the angle of incidence which is 60 must equal the angle of reflection so this side is 62 which means this is 30 now the three angles in a triangle must add up 180 so 180 - 110 - 30 that's 40 so the missing angle is 40 which means that this angle is 50 and according to the law of reflection this angle must be 50 as well which means that Theta is 40 so using the law of reflection you can easily find uh this angle let's try another problem so let's draw the picture first so let's say this material is air and then we have glass and finally diamond now let's say that light strikes the boundary between air and glass at a large angle of 60° and then it refracts into glass and then afterward is going to refract into diamond so what is the angle Theta at which it enters into the diamond material how can we find that angle feel free to pause the video and try by the way the index of refraction for air is one for glass it's about 1.5 and for Diamond it's about 2.4 so let's solve for Theta 1 or let's call it Theta 2 let's say Theta 1 is 60 so using sel's law N1 sin Theta 1 is equal to N2 sin Theta 2 so N1 is 1 and then we have sin 60 which is equal to N2 that's the value for glass time sin Theta 2 so let's solve for sin Theta 2 sin Theta 2 will be equal to sin 60 / 1.5 if you type that in the calculator you should get < tk3 over3 which is about 577 so Theta 2 is the inverse sign of 577 so you should get 35.262781 equal to N3 sin theta 3 so the second index of a fraction for glass is 1.5 time sin Theta 2 which is 35.262781 .26 / 2.4 and so this is equal to 36 and the inverse sign of that answer is 21.1 De so that's the value of theta 3 so notice that the angle between the normal line and array it decreases as n increases so here we have a small value of n but the angle is very large and as n increases the angle decreases here n is very high but the angle is the smallest of the three by the way another way in which we could find theta 3 directly is instead of saying N1 sin Theta 1al N2 sin Theta 2 we could say that N1 sin Theta 1 is equal to N2 I mean N3 3 sin theta 3 so let's say if you only want to find this angle and you really don't need to find Theta 2 you can go directly to theta 3 um by using uh just air and Diamond you can skip glass so let's try it that way so N1 is 1 and Theta 1 is 60 n 3 is 2 .4 and let's solve for theta 3 so sin 60 / 2.4 that's 3608 and theta 3 is going to be the inverse sign of 3608 and you get about the same answer which is 21.1 De so even if you have multiple materials if you need to find the last angle you can simply go directly uh to that angle using the first one so let's say if we have multiple materials let's say on top it's air and then we have water and then it's GL glass and then let's say plastic and Diamond at the very end so let's say light strikes the surface at a 70° angle and then it refracts into these surfaces so what is this angle let's just call it Theta how can we figure it out so even though we have multiple materials in between all we need to focus on is the first part and the last part air and Diamond the index of refraction of air is one the index of a fraction of diamond is about 2.4 and so that's all we need so in this case we could say N1 sin Theta 1 is equal to n 5 sin Theta 5 so 1 * sin 70 is equal to 2.4 time we'll just call it sin Theta sin 70 / 2.4 that's 3 915 so to solve for Theta we need to use the inverse sign function so inverse sign of 3915 that's about 23° and so even though you have multiple layers of different material you just need to focus on one material the one that you have the information for and the one that you're looking for so if we want to find the index of fraction or the angle for let's say glass we could just use air and glass we can skip water we can find the angle for any one of these if we just focus on that material only let's try another problem let's say that this is a block of material and the index of a fraction is 1.2 and outside we have air which has an index of refraction of one now let's say light strikes this boundary at an 80° angle and then it refracts into the material and then it escapes back out into into air what is the angle Theta go ahead pause the video and see if you can get the answer so let's use Snell's law to find Theta 2 first so N1 sin Theta 1 is equal to N2 sin Theta 2 N1 is one for air and the angle outside is 80 and two that's going to be 1.2 time sin Theta 2 so sin 80 / 1.2 that's about 8207 that's equal to sin Theta 2 so Theta 2 therefore is the inverse sign of 82 7 so therefore Theta 2 is about 55 2° now notice that we can turn this into a right triangle and so this is 90° to find the other angle it's going to be 90 minus 55.2 and so this angle here is about 34.8 de so now we can find this angle which we'll call theta 3 so N2 sin Theta 2 is equal to N3 sin theta 3 where Theta 2 is a different angle it's 34.8 instead of 55.2 so N2 that's the index of refraction for the material that's going to be 1.2 Time s of 34.8 that's equal to N3 which is associated with air which has an index of ref fraction of one * sin theta 3 so 1 .2 * sin 34.8 that's going to be about 6 849 and that's equal to sin theta 3 so theta 3 is the inverse sign of 6849 and so the final answer for this problem should be about 43.2 de so that's the angle at which light is going to emerge out of this material and on the other side try this problem the speed of light in ice is 2.3 * 10 8 m/s what is the index of refraction of ice so the equation that we need for this problem is V is equal to C / n we have V that's the speed of light in a different material and N is the index of a fraction of that material C is the speed of light in a vacuum so you got to solve for n so let's rearrange the equation Let's cross multiply 1 * C is C and V * n that's just VN and then if we divide by V the index of refraction is the speed of light divided by it's the speed of light in a vacuum divided by the speed of light in the material so it's going to be 3 * 10 8 / 2.3 * 10 8 we can cancel the 10 to 8s so all we need to figure out is the value of 3 ID 2.3 and so it's about 1.3 so that's the index of a fraction for ice as you can see it's very similar to water which is 1.33 a certain light Ray has a wavelength of 400 NM in glass what is the wavelength of this light in Diamond what equation do we need for this problem so if you have one wavelength and you want to find another you can use this equation Lambda 1 / Lambda 2 is equal to N2 over N1 so let's say Lambda 1 is 400 nanom we're looking for Lambda 2 now Lambda 1 corresponds to N1 so the 400 nanm that wavelength is associated with glass and the index of refraction for glass is 1.5 the index of refraction for Diamond which is associated with N2 that's about 2.4 so now all we need to do is solve for Lambda 2 that's the wavelength of light in Diamond so let's cross multiply so it's going to be 2.4 * Lambda 2 and that's equal to 400 * 1.5 what's 400 * 1.5 400 * 1 is 400 400 * .5 or half of 400 is 200 if you add 400 and 200 you're going to get 600 now we just need to divide both sides by 2.4 so 600 / 2.4 that's about 250 so because Diamond has a higher index of refraction than glass the wave length in diamond is going to be lower than that in glass it's going to be less but this is the answer so you just need to use this equation so that is it for this video thanks thanks for watching and have a great day