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When light goes from material with smaller index of refraction to 3 material with a larger index of refraction total internal reflectionwill never occur;will occur ...

Question

When light goes from material with smaller index of refraction to 3 material with a larger index of refraction total internal reflectionwill never occur;will occur [ the angle of incidence small cnoubh;will occur if the anglc of incidence Iarge cnough;

When light goes from material with smaller index of refraction to 3 material with a larger index of refraction total internal reflection will never occur; will occur [ the angle of incidence small cnoubh; will occur if the anglc of incidence Iarge cnough;



Answers

When light passes from a more-dense to a less-dense medium—from glass to air, for example—the angle of refraction predicted by Snell’s Law (see Exercise 81) can be 90 or larger. In this case, the light beam is actually reflected back into the denser medium. This phenomenon, called total internal reflection, is the principle behind fiber optics.
Set $\theta_{2}=90^{\circ}$ in Snell's Law and solve for $\theta_{1}$ to determine the critical angle of incidence at which total internal reflection begins to occur when light passes from glass to air. (Note that the index of refraction from glass to air is the reciprocal of the index from air to glass.)

This question. We have three materials. The light goes from material one to material too. And with the angle off incident, Peter and the angle off. Ah, refraction iss the quick Kono, as I say in the question, inside material too. And they want to know what is the angle, Tater, We can find these using the law for fraction so and one and one signed Tito one Santeria here is equal toe end too. So the complimentary angle big coast side off the critical. So there's a sign off nine degrees miners and did the critical. So this is sy off 90 mindset a critical on because this is the critical angle we can relate to entry and to buy this relation here. So this gives us and we are using that and one is here. So signed off, Peter, is this going to end too? Course sign off Critical. And this this and two square root off one minus and three squared, divided by two square There's this square root off and two square manners and three square. So this gives us That's right here Waas. So you know, a sign minus one of sway rode off into square minus and three square. There's this sign minus one of square root, and two is 1.4 and three is 1.2 1.4 square in minus. Won't buy to scratch. And does this 26 0.8 degrees for part B. They want to know what happens. When were you increase there. They're asking if there is refraction off light into the material trip, so increasing terror will decrease the angle in which the light strikes The interface between two entry so he began, becomes greater than the critical angle. So they will be transformational flight here. So if you increase here, we start best light here. It's a dealer. The bar is a very talented, so increasing theater. There's anger. Okay, here will decrease and then will be. They go here, be greater than the quit going Go. This means that there will be refraction off light into material tree

Ah, trees, different materials. And we shine a light through the first material. And we they're like, passes through the second month you and undergo a total internal reflection in the surface between the second and third material. And we know the initial angle here in the first refraction. That is fine. The first thing that they ask is toe complete the index off a fraction and three. So for this we can use that the angle here at end too. It is a total internal is a total and go off off interest. Sexual. So we have that and three divided by anyone. Yeah, me too. And I am too is equal to sign of critical angle. And so far, the critical ago and the critical and will be exactly a goto the internal and go here. Five so fine. So if I Is it cool, let's solve it for entry. So, entry, is he going toe end too? Signed off Fine. And there's this 1.6 cy 60 degrees. This is one point every night. So this is for part okay for part B, they want to know the angle, dear to know the angle it either we can use the first refraction that, of course. So let's use the law for fraction there in this between the interface off material one and two. So the loss of a fractional be end too Signed off. But in degrees, the complimentary angle off 60 A sickle toe end. Well, sign Bastida. So we get that sign off. Data is you could tow end two divided by anyone. Sigh off 30 degrees. And if we so for theater data is 28 0.1 degrees. The last part. They want to know if we decrease the angle. Tita, those air like to refract into the material three. So the increasing that angle teeth that were increased their go five and make the race strike the inter fest at the angle larger than the critical oil. So there will be no transmission off light because they angle here, Be larger than the critical who Accordions. Mission flight. We have to have that. The angle in the surface last in the critical oil. But this is the answer for the part. See

The first step is to apply Snell's law at Point A in order to figure out what the critical angle is. And then we'll fly Snell's law above that in order to figure out what the incident angle must be. And so first, we're going to play today. Apply. Snell's Law Day gives 1.38 This is the index inside time, sign of the critical eagle, and this is equal to the index on the other side, which is just air. And since we're at the critical angle, this is nine degrees. This lets us all for the critical and ends up being 46.4. Where we do this out, bro. This is actually in different seas there. So sorry about the sloppiness. This is 46 plus four degrees. Now that we know the critical angle, we know what angle we must achieve with the other cells law, and that allows us to find the angle of incidence that we must have to achieve. This is around billing Eagle, And so what's up ourselves? Law again, say Toby, which is the refractive angle here is related to the critical angle, about nine degree offset since their compliments with respect to each other. And so we have this relation here and then playing in 46.4, we get 43.64 stay, Toby, This is our actual refractive angle. They were about to use for a second skills along. And so let's go. And for God in 1.0 for in one time. Sign of our incident angle. Hey, this is over. Solving for is equal to the new index. 1138 time. Sign of the refractive angle which we just found here. 43.6 degrees. This gives state eh is equal to 72.1 degrees, and that's the answer.

In this problem we have to calculate the minimum value for the index of refraction of the fiber. Let the index of reflection of the fiber is. And yeah so what this is the fiber where this light beam is directed with an angle of uh I this is the angle of incidence that point and that uh and the beam reflected through this fiber and it makes an angle of this will be 90 degree minus theater and this is the angle hit at point B. Let's apply this uh let's apply this landslide two point. So for that case we can wait an air science to die is equals two. and sign of my interrogator administrator. This can be for the region as an air Scientific to I is equals two. This can the region has an into yeah signed 90 degree cousin of theater minus cosine of 90 degree sign of theater. Now in this case we know that this sign 90° equals to one and because I know of 90° equals to zero. So we can simplify this equation as an air sign of theater I is equal to. And because I know theater So this will be our equation number one. Yeah applying the strength slide point to be we can white the equation for the critical angle as and sino teacher Z equals to an air. So this will be our equally number two. Mhm. Now using equation number one in the equation about you, we can white equating for this. Uh And as a let's right and square air into one plus Science square of today is equals two and square into science square theater plus go Science Square theater. So this will give us the identity that is equal to one. So from here we can write the equation for this uh N as N E. Z equals two and there squared of one plus science squared hit. I okay now for the minimum value of end we can set the minimum value for the Science theater. I so let's assume that this sign three D. is equal to -1. So From here we can wipe this equation as any z equals two. 1.000-9 into squared off one plus minus one. Well square. So this can be written as any Z equals two into 1.0 to 9 into squared off one plus one. That is equals to two. So here we will get to From here we will get the value for this end as any z equals two 1.41. So this is the minimum value for the index of refraction of the fiber. Thank you.


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