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A laser produces unpolarized light of intensity Io that is incident on a series of polarizers. Referring to the figure, suppose that angle filter 3 is at a general ...

Question

A laser produces unpolarized light of intensity Io that is incident on a series of polarizers. Referring to the figure, suppose that angle filter 3 is at a general angle 0 with respect to the vertical, instead of 90 degrees. (a) Determine an expression for the transmitted intensity as a function of 0. (b) Plot your result from part (a) and determine the maximum transmitted intensity. (c) At what angle does maximum transmission occur: (d) Repeat part (c) for a different configuration where filter

A laser produces unpolarized light of intensity Io that is incident on a series of polarizers. Referring to the figure, suppose that angle filter 3 is at a general angle 0 with respect to the vertical, instead of 90 degrees. (a) Determine an expression for the transmitted intensity as a function of 0. (b) Plot your result from part (a) and determine the maximum transmitted intensity. (c) At what angle does maximum transmission occur: (d) Repeat part (c) for a different configuration where filter 3 is left at 90 degrees and filter 2 is free to rotate_ 309 3 = 909 A B 3



Answers

Unpolarized light of intensity $I_{\mathrm{o}}$ is incident on a polarizer-analyzer pair. (a) If the angle between the polarizer and analyzer increases in the range of $0^{\circ}$ to $90^{\circ}$ the transmitted light intensity will (1) also increase, (2) decrease, (3) remain the same. Explain. (b) If the angle between the polarizer and analyzer is $30^{\circ},$ what light intensity would be transmitted through the polarizer and the analyzer, respectively? (c) What if the angle is $60^{\circ}$ ?

Okay, so this problem is similar to a problem. 79. And we have tree futures trip polarizer futures their first future as an angle that's called Teeter Off zero degrees. We have a second polarizer with angle off 30 degrees with the vertical, and we have a turd polarizer with an angle that we do not know. So let's go this final and go or simply Tito. This is just a detail. So the first question of this problem, we have to described intensity. Final intensity. Let's call white tree off the being off a being of light after this being passes from this street. Well, risers. So first of all, let's just remember that after passing for the first polarizer since the bean off light is, um, polarized light, we know that why one? It's going to be the initial intensity, Which is why not if I did by two. So, um, polarized light after passing through any type of polarizer has is absolute intensity decrease by half. So this is the intensity off the vino flight. After pressing for the first polarizer, the intensity after passing to the second polarizer is just y zero divided by two multiplied by the cosine square off the angle, which is 30 degrees with the vertical. So we have after calculating this, we have a value off 2.3 75 Why not? And what is the final intensity off? This being of light is just zero point 37 five. Why not multiply by the casino square off the angle between the second polarizer with turned polarizer? So this is just Tito minus 30 degrees. So this is the answer to the first itin of this problem We have to describe on equation of function off the intensity in function of the angle. So here we have here we have this function. So this next item of this problem so I can be we have to plot a graph for or dysfunction. So let's begin here with the excess. The why excess it's going to be do intensity and the ex excess. It's going to be d angle. So we have a function. Define us Bye equals, you know point 37 five. Why not the multiplies? The cuisine is square off teeter minus already degrees toe blood to this graph First, we must know that the amplitude off this function is defined by this value in here. Zero point 375. Why not? So the maximum value off this graph should be here, Which is going to be, you know, point 375 Why not the minimum value off this graph? Since this is a cuisine square is zero. So he's the zero. Therefore, we know that this function, the lot of dysfunction, should be limited to the strange in the intensity excess. Now we know that the graph for Corzine has his maximum value when his argument is Ciro. Therefore, we know that casino zero is one, but this Christine is shifted from 30 degrees. Therefore, we can say that here in the point, it's already we have to maximum value off the coast in square. And the minimum value is when this argument is equal to 90 degrees. But this is also shifted. So we can what didn't 90 around here, for example. So since this is 90 degrees, we know the minimum value minimum value also is going to be shifted by 30 degrees. So we have something around here. This is the minimum value. Therefore we can know begin to Graff because we know that his maximum value should be in here and hiss medium Virender should be. And here therefore, we can we know that how to catch r cosine, Griff. So this is something like this. It's just a minimum value, and the graph goes up again, stops in this range here and then goes down again and continues to do the same behavior for all. Tita. So this is this catch off the graph? Uh, the final question of this problem. The final question we have to describe In what way? What angle? The maximum transmission occur so the eye can see. We just have to describe what angle has the maximum transmission. We already told you what it is. We know that data miners attorney degrees should be equal zero. Therefore, we know that the angle should be charity, the grease. So here we have the maximum value, you know, to know the other point with maximum value, we just need to pick the Tita, which is sturdy, and some ad 180. We should gives us 210 degrees. This too. Our maximum values off the deters meted intensity of the light. And that's all Thanks for watching

How are your first forgiven? Mm anger Vita Evan is 45 minutes theater, too. 90 degree theater. We went 45 degree theater veto Jiro degree theaters, even 45 million. Three to Zito, minus 45 degrees. So I was scared to I polarized causes square theater on this consent. This problem is based. So in case a I horses square 45. Any case B just to me cost you square off 45. In case you see, it is courses square of 19. So a scared Tobey, it's greater than you now be part in 10. 34 is e. Who believe are you not courses square suitable. And two courses square theater to my nesting cover. Yeah. Substitute 50 point point five. Of course. The square of 45 and two causes. Fire off 19 minus 45. So check in 0.9. About 4 m square in case of be analyzed it. I am not 55.5 causes square of 45 courses square off zero minus 45. So it is 13.9. What per meter square in case of analyzer. See 50.5 cause the square of 45 courses square of minus 45 minus 45. So it is zero. Yeah, their son. Thanks for

Okay, So this problem we have an incident being of light with an intensity. Why not? That is here. The passes through a polarizing future. Transmission access is at an angle, Tita to the vertical. The first thing we need to calculate here. The first item. Actually, I thin a We need to look to the curves in the figure hence and give the caller off the curve represents an, um, polarized light. So we know that the n e m polarized light when passes fruit, any type of polarizer should be decreased by half. So we can say that the curve should be green curve because, um, polarize it light. We'll always be reduced in intensity by a factor of two, regardless off the angle off the transmission excess. So always remember this the first item should be green. The fight in me should be red because at Tita equals zero we have completed. We have complete transmission, meaning that the light is vertically paralyze it. So we have the maximum value in the red and the final item can be on Lee be Luke. Because when Tita Eco's zero, we have no transmission, which means that the incident light is horizontally. Paralyze it. So we have a medium on value. And that's the answer to this problem. Thanks for watching.

In this part of their case, we will have I three. It was I do well saying squared this just we write it from the big very beginning I three equals half off. One for half of I not is I want might have died by for science for 45 degree gives us i to multiplied by Poseidon Squared 45 degree minus 30 degree gives us I three So can bleeding. We get place to be 0.233 I not says so. I three equals 23.3% off. I know now, In the second case we have after the first polarizer The intensity is half I not and this is I wan and I do. It was this must abide by Poseidon squared 30 degree on that gives you I do so that is suitable. And 375 I not it was 37.5%. Oh, why not


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