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4lig 40c4 35E. grating has 400 lines/mm: How many orders_of the entire visible spectrum (400_700 nm) can it produce in a diffraction ex- periment; in addition to th...

Question

4lig 40c4 35E. grating has 400 lines/mm: How many orders_of the entire visible spectrum (400_700 nm) can it produce in a diffraction ex- periment; in addition to the m 0 order? ssm ilw Ales

4lig 40c4 35E. grating has 400 lines/mm: How many orders_of the entire visible spectrum (400_700 nm) can it produce in a diffraction ex- periment; in addition to the m 0 order? ssm ilw Ales



Answers

A grating has 400 lines/mm. How many orders of the entire visible spectrum $(400-700 \mathrm{nm})$ can it produce in a diffraction experiment, in addition to the $m=0$ order?

Okay. We're told that D straight down here is 5000 lines per centimeter. One over 100. That's going to be 1 5/100 of a meter between lines. So, um, we look at the equation. I m lambda equals de signed data. Now it's gonna have the most difficulty reaching the highest wavelength. So I'm gonna set Lambda equal to 700 nano meters and so and equals d Sign Fada over Lambda, where sine theta is gonna be its maximum, which is one, um so I'm gonna write em is less than are equal to de signed data where science data is one so d over lambda. I'm gonna put that in a calculator. One over 500 1000. I need to divide that by 700 times 10 to the negative ninth power I get em is less than or equal, Teoh. Two point. Let's see. Got three significant digits here, 86 So the answer would be two of them. We don't quite get to the end of the third

36.1 12. We want to know how many orders a diffraction grating with 500 lines for millimeter is going to produce that include the entire visible spectrum. First, the of course is the universe of this. That is, uh, two microns. Now, there could be no refraction angles greater than 90 degrees. And so we should just worry about the largest wavelength. The 700 meters toe. Find the maximum here because it'll this it'll go. It will be the first to go. Azi order increases so de times sign of 90 degrees because that's the maximum that could be invited by are 700 nanometers because this will be the first go past 90 degrees as the order increases. So this is just be over. I am, uh and this is something a little bit over to, so just taking the the floor of it, rounding it down, whatever. No, it's going to be too. A sort of fractional values of em you can think of is being not quite getting to the next Pekar minimum. So if you wanted, if you want the complete, you want an actual like beak. Um, it has to be an integer and then you have to go down from whatever something like this is in order to get an interview, you can go up to the next because it won't be that.

To solve this problem for us, we need to find out the separation between the street and these equivalent uh one m or tenders minus two m for one centimeter. Upon the number of flights. That is 5000. So from this we get the separation between the two adjacent slater's uh two and two tenders minus six m. Mhm. Now for the faction grading for uh bread specter line, the sine theta. Is that cuba rental? I'm linda. Are the maxim order M. Canberra, tennis the scientific to upon linda. So for the maxim order 3 to can be 90°. So the maximum order D. M. Is equivalent to doing two tenders minus six m into one upon the wavelength that is 412 nanometers or 412 into tenders minus nine m. So the value of m the maximum value possible is 4.85. So the maximum order is a Cuban into the food. So for the world light, the maxim order for the spectral line through the defection rating is for

Certainly this question. We have grating off non separation, and we will pass a grating with white light. And we know white light is a mixture of different monochromatic lights, so this white light have lights with wave. Lis is ranging from four hundred nanometers is seven hundred meter and were asked about how many spectral orders can be seen. So what does this mean? Because So equation we have his dear science Seder horse and Linda, or if we rearrange, is because it's asking for special orders. That is ten m equals descend Seita over Nanda. So if we look at this because we already know D, we already know the legend Ranch off Linda, and we know science data has to be smaller or you go to one. So because of that, I am is not infinitely large. SAT means the pattern on the screen for disappear after a certain amount of orders. So for white light, what will happen is if you have the diffraction grating over here, we already know that you have a pattern end from dealing ways. Double slit reflections in the crevasse sections. We knows that a longer wavelengths light usually has more spread out patterns so short away place wass so longer. With this one will be more like this. It's living more spread out, and if we also just look ATT, says Expression, we're sees that I assume we have the same d into thing science. Ada. Well, damn, Doc, it's larger and gets smaller. So that means for longer way plans. Is it? Were exhibit Fear were order, since all squeeze shut away places so you might be able to see Sai. Three others for the Blue died, but you'LL only be able to see two orders for the red light just as an example. But so when's the question asked us how many special orders can be seen? It is asking us how many complete orders can be seen. So when we have the white flights that has wait, bless all the way from four hundred and thirty seven hundred meter, So are we can be seen is limited by the minimum order, so it's limited by the longest witness. It's the longest reverence. You can only see one order. It doesn't matter who how many are common in Orissa. Conceive for us with places because then they are not complete, you won't be able to see the full spectrum. So because of that we're using Lambda equals several hundred animator here because that's the limit we have. That's what this was constraining us from having a complete spectra. So was that miss picking the numbers? The maximum I am. We have to use Maximus science data. So that is just one. So d is. It's one centimeter over seventy four hundred slits. And if I want to write it in terms of meter just like this, is there a point? Several Want meter Sam Seder. It's just one because we're looking for the maximum. Linda is seven known earlier. This gives us one point nicely. So this diffraction grating really only give us water for order all the way out to read a sentence. One complete order. So that is all we can see on each side of sensual, which light. So this crap, it's not right because we can really just see one of these each side of the white light, and we can see that if you're interested, you can calculate it for four hundred army, don't you? So you can see that we can actually see blue light up to a few more orders and actual where you can almost see the red light for the second order. If we just cut, we almost can't. But we got it. But so the second order is almost fully visible, but we do not have a visible. So that also is one no.


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