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18.10 pts possibleLaser light of waveleriglh 375 nri is shone thrcugh singl shtapparatus [nal spaced cistarce 75 crti ftOrt scieeri; difraction palterri results on ...

Question

18.10 pts possibleLaser light of waveleriglh 375 nri is shone thrcugh singl shtapparatus [nal spaced cistarce 75 crti ftOrt scieeri; difraction palterri results on the screen with an observed central wicth maXirTUr of = [TT Whar is the width ofthe slit?188 prTh752 prth4. 47 pmti5. 65 piti268 pr)427 Ur128 prT)376 pr94 pMTI

18.10 pts possible Laser light of waveleriglh 375 nri is shone thrcugh singl shtapparatus [nal spaced cistarce 75 crti ftOrt scieeri; difraction palterri results on the screen with an observed central wicth maXirTUr of = [TT Whar is the width ofthe slit? 188 prTh 752 prth 4. 47 pmti 5. 65 piti 268 pr) 427 Ur 128 prT) 376 pr 94 pMTI



Answers

Laser light with a wavelength of 632.8 $\mathrm{nm}$ is directed through one slit or two slits and allowed to fall on a screen 2.60 $\mathrm{m}$ beyond. Figure $\mathrm{P} 38.42$ shows the pattern
on the screen, with a centimeter ruler below it. Did the light pass through one slit or two slits? Explain how you can tell. If one slit, find its width. If two slits, find the dis- tance between their centers.

What else? To give a problem. The angle from the central maximum to go first. Fast, bright, bright friend is bridges is given by D Sign their top, right, Right. Physical tow n times a Linda from here. Ah, fate up for first bright fringes and musical toe One for first Brian Fringes right Will be signing worse. Oh, for M times Linda divide by D Some student your values we have here Sinan Worst musical one. So Lamda easy trees 6 33 uh derided by 1.45 times Don't bother. Minus minus five. This gives us an angle for the first right fringes to be, um, heard off 2.5 degrees. But be the angle from central max to the second right second darks only know the bright dark fringes is given by again the formula that he signed Do you sign data? Dark is equal to M plus one or two times. Linda, where I am is a call to one for the first our trainees tools of student value in Seoul for a better so they had the dog will be signing worse off one plus one or two. So shooting the value for Linda, that is 6 33 times 10 to power minus night, derided by 1.45 times 10 to power minus five. So trying this time we get the data. Ah, the angle from the central max to a second doc. Fringes to be 3.75 degrees. What? See, uh, the distance off. The first bright fringes from the central max is given by why bright is equal to lend at times. L divided by tee times him where I am is a call to one we confined. Why? So why will be why bright will be Lambda, which is a 36 33 times than our minus nine times two, divided by 1.45 times didn't about minus five times in musical. The one this uses Why to be 8.73 centimeter. The distance from the first bride fringes from the central max is 8.78 point 73 centimeter

For this problem. On the topic of wave optics, we are given the wavelength of laser light, and we're told that it's directed either through one or two slits and allowed for on a screen a given distance. Beyond were then shown the pattern of the on the screen with a rule below it. We want to know if the light passed through one slit or two, and then if the answer is one slit, we want to find the within that split. If it is two slits, we want to find the distance between the centers of those two slits, so we can see immediately that the light has passed through a single slit, and we can tell that it's a single slip because the central maximum is twice the width of the other maximum. So the space between the centers of the success of dark fringes and in a double slit experiment double slit pattern, the central maximum will have the same way as all other maximum. So since this is a single split, we know that in single slit diffraction, the width of the central maximum on the screen is given by the following equation. Delta. Why of the central maximum is equal to two l times the 10 of data dark. So the first dark fringe aim is equal to one, and this is approximately equal to two l times or a small angle. This is approximately sign data with him equal to one which we can write as to our times one and the Waveland Lambda over a which is equal to two into Lambda L over a meaning that we can rearrange and find the width of the slit, which is a and A, is equal to two lambda l of a delta. Why so substituting our values into this? This is two times the wavelength of the laser light 632 0.8 times 10 to the minus nine meters times the distance to the screen, 2.6 m times delta y, which is 10.3 minus seven 0.6 centimeters, which we can see from the ruler. And we need to convert this 2 m. We multiply this by 10 squared centimeters for every meter. This gives us stay with the slip to be 1.2 times 10 to the minus four meters, which is 0.12 millimeters

So in this problem, laser light off web links 632.8 nanometer hits Either single sleep or double slid that we don't know yet. The diffraction patterns form at a distance 2.6 meter from the slit. The figure 30 to 38.48 in the statement of the problem shows the diffraction pattern and the distances between them with a centimeter centimetre ruler there. So in problem a the part A of the pred been in part A. We want to find out whether the diffraction pattern corresponds to the single sleep or double slate. Now, since the wit of the central maximum seems twice as wide as the other ones, the slip used must be single stlede. Okay, so I'm gonna write down singles laid here. So this is the answer, but also to reinforce our claim. The double slit Maxima are even this evenly spaced, which it is not the case here in the figure. So this make sure that sleet that was being used is single sleep. Now, in part b of the experiment, the part b of the problem. To find the weight of this late, we find the distances between the two second Maxima furs. And it is two y just following the figure to why I was just a different distance between the to second order minimum. Okay, then this is gonna be cool to 11.7 centimeters, minus 6.3 centimeters, which is going to give us 5.4 centimeters. That means why the distance of the second minimum from the center of the central maximum is going to be called to 5.4 over to which is 2.7 centimeter. Now, I'm gonna write this in terms of meter, which is 2.7 times 10 to the negative. Two meter? No, from 10 data to equals. Why? To over l remember. You have sleep here and the screen here. The second order diffraction forms here, and this is the angle. There are two. And this is the distance from the central maximum to the second order minimum, which is why to and this is the distance between the slit and the screen. Right? So from here, you can see that the 10th out of two equals four I to a Braille. So I'm here that are too is going to be called to 10 in verse. Why? To over L, which is 10 in verse. Why two is 2.7 times sent to the negative too. Over. L was 2.6 meter and this is going to give us syrup 0.595 degrees now, using the condition for the third order diffraction minimum for a single slip with actually the 2nd 2nd order diffraction minimum. We can use a sign. Data two equals tool NMDA, right. This is a condition for the single slid second order diffraction minimum. So from here, you can see a is going to be called to Lambda over. Scientist to two Lambda over. Sign data to we know the value of scientist or two now. So this is gonna be to time slammed out of the Web link waas 632.8 net readers over ST in a two is sign off 0.595 degrees and this is going to give us 1.2 times 10 to the negative four meter or you can also say 0.12 millimeter. So that's the weight of the sleep being used as a single

Wei have. Ah, and, uh, Parcher offered 0.0 250 millimeters. The violent incident is 632 0.8 now. Witches, We want to find out the We are also given that I notice it will do 8.50 water meter square. You want to find out the total number off orders off direction? We know that scientist is it called Homeland of I D. I mean, as a scientist, I can have a maximum value off one which corresponds to a musical do evil Landa It's turns out to be they don't want to go to five into the entire ministry derided by 6 32.8 into Denver minus nine which is 39.5. Which means there are 39 orders off Maximus and so many of us 45 We want to find out the last bright French. So for that we want to find out the 39 38 minimum and then approximate that this midpoint corresponds to the last write French. We know the data scientist is equal to embalm the body, which means Tito physical to Sinan, Worse off and land already so the Tito corresponding toe 39 doctrine JJ, don't tell Toby 80.9 degrees on the teeter response was fined 2 38 degrees 38 Dr. Finch corresponds to 74 5 one degrees. So the main point will you respond to the outage? We just 77 points. Five degrees? No. So at this angle we know that Vita is equal to five Landa decent ITA. So that is two time by 6 32 0.8 into 10 ten four minus nine Distant deal which is 25 into 10 minus six Santa just signed 77 45 It's turns out to be No. Yeah, a very large number. Let's call this Peter. So we know that I is equal to or not signed by you squared by whatever do square on by Simply plugging this into a calculator will see that this is equal dough. This gives Isaac, although Einar times 1.6 cylinder into a 10 5 minus six. We know that that I not Izzy caldo. We don't know that I'm not is equal to 8.5. What when we just quit. So simply were multiplying this with 1.67 into 10 minus six. We see that it is equal to 1.4 into 10. Power minus five. One point for doing duty in four minutes. Five water for me. Just clear. This is the intensity off the last bright French approximately.


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