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Least Time A beam of light propagates from point A in medium 1 to point B in medium $2,$ as shown in FlGURE $26-78 .$ The index ofrefraction is different in these two media; therefore, the light follows a refracted path that obeys Snell's law. (a) Calculate the timerequired for light to travel from A to B along the refracted path.(b) Compare the time found in part (a) with the time it takes forlight to travel from $A$ to B along a straight-line path. (Note that the time on the straight-line path is longer than the time on therefracted path. In general, the shortest time between two pointsin different media is along the path given by Snell's law.)

(a) 506$n s$(b) 510 $\mathrm{ns}$

Physics 103

Chapter 26

Geometrical Optics

Wave Optics

Rutgers, The State University of New Jersey

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this question way Have a beam of light propagate from point A to point B toe medium. Then I want to show. Went to, uh, compared, er time taken for the light to travel from point A to point B. Uh, in this reflected path, it will take less time. Then when the light takes the straight line path came a short. Okay, so, uh, in part, A, we want to calculate the time taken for the lights to travel along the refractive puff. So to do this, um, again, it involves now slaw. And we're also going to do something. Uh huh. Time calculation. Okay, so we are going to call this distance D one and this distance distance D to. And then we're also going to call this anger the data to, um and then, um, so reading to find data to first. Okay, So using snow slaw on one sided one, does he go to end two sided tool? Uh huh. So excited to is equal to so, and one is one and they don't want is 45 degrees and developed and to which is 1.4 and cooperate this against 0.505 And so data to Is he going to 30.3 degrees. Okay. And, uh, so we need to calculate, uh, d one and D two. So we have these two triangles, and this is 45 degrees is the one, and they have another triangle. It is 52 then this is data to Okay. Okay, so we have one equals two eso. This is like 10 m. 15 years. Okay, So, based on this information, we have, uh, the one is equal to 50 right by, uh, cause I 45 degrees. Okay, then P two is equal to 15. Defined by who's I, uh, the deacon. Tree degrees key. Yeah. Then you can find the time taken the time taken for the light to travel along the refractive puff. Okay, so this is equal to, uh you want derived by B one plus into developed by me too. Okay, So the one is 50 different by design for five degrees, and everyone is the speed of light. Mhm flash. Uh, he, too, is 15. Divide by preside The country degrees, then the speed off lights in medium to let's see divide by N p. So you calculate this Substitute the speed of light. Uh, into it. So? So we have 50. Divide by. Let's be off light three times. 10 to the eight. Yeah, 1/45 degrees plus 1.4. The rabbi course. I, uh, that you 0.3 degrees cockpit. Did you get 506 nanoseconds? Mhm. So this is the answer for Poppy. Okay, next in part B, um, I went to find the time taken, You travel along the straight line path. Okay, so this history line path Yeah, I'm going to call this d tree key. So? So, D tree country. Hey, follows this triangle. Okay, 100 m. Yeah, and then, Ah, 45 degrees. Okay, So, um, tea tree. Is he good to? I read the rabbi society. 45 degrees. You calculate years you get Oh, sorry. Wrong. It's not qualified degrees. Okay, so you need to calculate the tree differently. Uh huh. Okay, So first we need to calculate the a vertical distance that is not 45 degrees. Okay. Sorry. Okay. So first we need to find a vertical distance. Which is why, from a to B. So the vertical distance, all the vertical displacement, either. Vertical displacement. I'm from A to B. Did you go to, uh, 50 Tension. 45 degrees fast 50 engine, Uh, 30.3 degrees. Okay. How do we know that? So, um just now we have two triangles, right? P 45. 15. So this is this is one particularly space mint, and then you also have another triangle. Hey, this is a 30.3 degrees. Then the 0.3 degrees and then this is 15 years and we have a right to by one. Yeah. Yeah. So the particular displacement from A to B is actually. Why one, that's what two. Okay, that's why we are doing this. Eso 50 tension. 45 degrees class 50 30 country degrees, and you get 79.3 m and then the tree is the categories, um 100 square plus 79 countries square, square root, and you get 100 and 28 m. And then, um, the time taken for the light. Your travel along straight line path. Okay, so this is equal to okay. So, three over to in the first medium, which is one of the sea in the second medium. Just your end. Okay, So you recall that. Ah, at halfway decent Medium one. Hey, this is a medium to Yeah. So that's why I will be using the speed in medium one here and the speed of light in medium to Okay, so you simplify you get you to and plus wanna. We'll see. Okay. And you have 128 m times one plus 1.4. If I buy two times. Three times 10 to the eight. A couple of days, you get 510 you know, seconds. Okay. So one thing is sure is that the time taken for the light to travel along the refractive parties? Shorter. Okay, then the shoreline power. Okay. And that's all.

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