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2.1 (14 pts) The following is the Jablonski diagram of ruby laser; the first laser:400 nmn550 nmnmetastable states694.3 nmi6934 nm2.L.1 (2 pts) Identify each transi...

Question

2.1 (14 pts) The following is the Jablonski diagram of ruby laser; the first laser:400 nmn550 nmnmetastable states694.3 nmi6934 nm2.L.1 (2 pts) Identify each transition (a) (d)2.1.2 (3 pts) The ruby laser has two emission lines_ 694- nm and 693.4 nm; Suppose you are at the surface of the sun (T 5800 K) What is the relative population cach state'2.1.3 (4 pts) You have 5.0 cm grating with 12,000 lines. The two emission lines strike the grating at an incident angle of 45.00 degrees. For the fi

2.1 (14 pts) The following is the Jablonski diagram of ruby laser; the first laser: 400 nmn 550 nmn metastable states 694.3 nmi 6934 nm 2.L.1 (2 pts) Identify each transition (a) (d) 2.1.2 (3 pts) The ruby laser has two emission lines_ 694- nm and 693.4 nm; Suppose you are at the surface of the sun (T 5800 K) What is the relative population cach state' 2.1.3 (4 pts) You have 5.0 cm grating with 12,000 lines. The two emission lines strike the grating at an incident angle of 45.00 degrees. For the first order, at what angles do these wavelengths diffract? 2.1.4(5 pts) If a screen is put 5.2 m from the grating, what is the distance between the two beams?



Answers

How monochromatic is a laser? The natural line width emitted by a collection of $\mathrm{Cr}^{3+}$ ions in ruby in thermal equilibrium at $290 \mathrm{K}$ is about $0.4 \mathrm{nm}$ for the 694.4 -nm line. This is the thermal line width. Show that the emission from a ruby laser is much more monochromatic than $694.4 \pm 0.2 \mathrm{nm}$ if laser emission is confined to a single-cavity mode. Take the length of the ruby between polished faces to be $10 \mathrm{cm}, n=1.8,$ and $d n / d \lambda \approx 0 .$ (See Problem 19.)

Hello, friends. Here it is given, like off a violent 5 20 nanometer that is 5 20 in tow, 10 to the power minus 9 m passes through regretting having 4000 lines per centimeter regretting having 4000 lines percent emitter and false on the screen located 1.6 m from the grating. So l is given 1.6 m in first part. We have to draw the diagram. So we is schematically represent the process and they will all known distances on angle, right? Be part angular Deflection for second bright went you tough work Second bright went See part right distance your separation off Second order right from central right French No to see it. This is the grating having 4000 lines and one cent emitted These are the wavefront off the light scrape at the distance off 1.6 m diffraction grating d to be one upon 4000 scientific er that is 2.5 micrometers. So with off the grating is 2.5 micrometers right wavelength is given 5 20 nanometer. This is central. Right? Finch first started second daughter and third order. This is why tree she the separation between the slits DS in the distance off one centimeter, there are 4000 lines. So it is to be 0.25 and tow 10 to the power ministries and Demeter, or 2.5 into 10 to the power when a 6 m and Guler separation for I met order. Bright French sign in Worse off, I am land up on the for second part. Angular separation off. Second order by French theater too. Sign in Worse off. Two in tow. 5. 20 into 10 to the power nine upon 2.5 in tow. 10 to the power minus six. It will be 25 degree the separation between second order Maxima and Central right French. Why, you will be, um lambda l upon the ed is Yeah. 1.6 m. Andi is 125 10 to the par minus six. So you will get by two to be 0.73 m. That's all for it. Thanks for watching it

Mhm. The radiance at a point P. Is given by I not by four. See you too. My inner city you gun. It's quite as you two minus as human square. Mhm. And two. See me too. Yeah minus E. V. But it's square because Yeah. Yeah asked me to as we would. It's quick. It's easy question. But here you I is to find us by I two upon Lambda are not the power hub and V. I. Is defined this did I. two Upon them are not to keep our heart. Okay. Since be point is aligned. You beat up center of the whole. Yeah. Be happy we want to sculpt a minus B. Two Gentleman is called to -2. Human is called- You too. We want is cooled to -32. So 1st 1st equation can be written ads. Hi please her to I not by four to see you too square two c. B2 sq into two seats. B to E script. Yeah. Mhm. Yeah. Okay. Plus two is they took square. Yes. Yeah. Yes. And further be, can be reassessed. I'm not by four bullshit. Youtube. Square Plus two Ways. Youtube. Yeah. Thank you. No, it's square. Yeah. His question # four. Yeah. Here right to is 2.5 mm. What by two skull to 2.5 mm. You will be 2.5 mm to a point 2 50 centimeter into 6 94.3 meaning the total power half. So it will be 272.70. So I p You can right 10. What? Per meter square upon four to see? 2.70. His square. Yeah. Mhm. Goodness, jewish. 2.70. It's square. Okay. How will the square So having it? You will get 9.39 bought four m square. Yeah. Mhm. They're so thanks.

Good as I could take a look. Good question. So he said, draw picture, not scale This scheme medically present. The process on their own on this senses angles. So on a given conditions, we know that the weight lenses by 29 meter and the great thing is with 4000 lines with per centimeters and the distance between screening and the grating is 1.6 meters. So sorry it's a graph for the first question. So there's a grating right here on the left side with bunch of limes, and it's interfering with, um, I know in a few waves, since there are so many splits, you know, raisins and its little so, uh, lines, and it's screwing on the rise I and the distance between the grazing and the screen is 1.6 meters. Eso this to some calculations here's so that we can make the A solution for the later questions will be easier for us to soft. So, you said, is 4000 lines per centimeters for the grating, and we can set ableto put on the lines. Oh, pretend toe number two beaters. Since one centimeters, it's 10 to the negative meters then we'll get four times 10 to the power of five lines per meter. And in order to get the separation between truthful is says, uh, it's a relationship. Off each lives is a relationship of the separation distance between each lions front of ratings. So we simply just put 1/4 times 10 to the by climbs a meter, which will give us 2.5 times tension xx Peter. So the separation off a slip off a double street, it's even the 2.5 tests tend to annex six Peter, and full question be We were asking us to determine angle deflection off the second driving. So remember the formula. Full anger, deflection. It's Saturday. I am because I m London, your body I m here is equal to two things. His second order, by Van Atlanta, is fight only now meter and these 2.5 times 10 to 1 and six meter with the separation of absolute. So just we know am musical to so simply discovery. Scientists, to which people two tons by 20 times tend to know tonight mirror because Wanatah meters is equal to tens of 99 meters and we are converting non meter two meters to make sure units is synchronized and so it's two tests by 20 times Central negative nine meters. Divide by 2.5 times. Tend to the name of six meter, which will give us 0.46 You were in order to figure out angry deflection, which is the Anglo data to view. We do, plugging the 0.40 point four or six backing to in verse. I function here and I will get the anguish about 24.6 degree, which is which is wrong about 25 feet. So for the last question, he was asking us to determine the separation of the second order bride spot from the central maximum. Okay, so there's a former for such question, which is why am equals two now does tension say that I am and we know that I am is equal to use the talking about the seconds or rib eye spot, so just simply Why, too? So why tell his equal to l tension data to and we know hosing down L, which is just the distance between the screen and the grating, which is 1.6 meters. So we're planning the data's you look something like this. So it's a 1.6 meters times engine 25 degree. And once we playing all these data to calculators, we'll get something like this, which is you see, uh, Boeing seven or six meters, which is 7.4. I mean, start 74.6 centimeters and less would be the answer for the last one. Thank you.

Hello students in this question we have given a transmission grating whose lines are separated by equals to 3.0 Marie claire bait. And to the power minus six m is illuminated by the narrow beam of red light. Having wavelength lambda not equals to 6 94.3 nanometer from a ruby laser. Okay. And we have uh the defected light is appeared on the screen at a distance R equals 2.0 m of it. So we have to determine how far from the central axis are the nearest sports. That is why. So from the first met from the diffraction grating, we have a sign tita M. This is equal to M. Lambda. Okay, So for the M. Is the number of maximum, so for the uh minimum separation so we can take this M equals to one. So we get A. And this sign tita M. This can be written as A. And this sine of theta. M. This from here, this can be written as why by radius. Distance are. Okay, this is the angle which will be substituted at a distance R. And this is equal to this one molecular lambda. Okay, so from here we get why it is equal to are arc sine of the lambda Driver Bay. So we can substitute the value. So our which is 2.0 m and arc sine of lambda, which is 6 94.3 10 to the power minus nine m Developed by a. Which is 3.0, multiplied by 10 to the power -6 m. So from here that stands why it is equal to 0.47 m. Okay, so this become answered for this problem. Okay, thank you.


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