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Diffraction pattern formed screen 90 cm owJy from from the center of the principal maximum 0.0003008420-mm-wide slit. donochromalic 546.1-nm light is used Calculate...

Question

Diffraction pattern formed screen 90 cm owJy from from the center of the principal maximum 0.0003008420-mm-wide slit. donochromalic 546.1-nm light is used Calculate the fractional intensity Illmaxthe screenpoint

diffraction pattern formed screen 90 cm owJy from from the center of the principal maximum 0.0003008 420-mm-wide slit. donochromalic 546.1-nm light is used Calculate the fractional intensity Illmax the screen point



Answers

A diffraction pattern is formed on a screen 120 cm away from a 0.400-mm-wide slit. Monochromatic 546.1-nm light is used. Calculate the fractional intensity $I / I_{\max }$ at a point on the screen 4.10 mm from the center of the principal maximum.

Okay, it's party question diffraction pattern is formed on a screen 21 20 centimeters away from the select. So L is given 1 20 centimeter and the birth of the cell. It is also given that is a cost to 0.4 mm. Okay. And monochromatic light having Wavelength Lambda is also given 546.190 m. Okay, so we have to calculate the frictional intensity. That is I divided by note. Okay. Be able to calculate on at a point on the screen that is 4.1 mm from the center of the principal magazine. Um it means why is given 4.10 mm. Okay, so we know that I divided by I not That is the fractional intensity. Okay. That can be calculated by sign. Better by two. Divided by bitter by two. Holy Square. Okay. We are built to is the phase difference from the top and the bottom portion of the slate. Okay. And we also know that be to buy two can be calculated by pi a scientist to divided by lambda. Okay, so no problem. We will find out data by two. Soap I spy is given that 0.4 mm it will be 0.4 multiplied by time raised to the power by an extreme eater. Okay, santa And scientists will be Why by L. Okay. Uh, why by L. So why is 4.14 point one multiplied button raised to the power minus three m. Okay, bye bye. L at least 1.20 m. Okay. 1 20 centimeters and divided by lambda is also there. So lambda is given 546.1 nanometers attendees to the power negative nine. Okay, so when we saw this will be 7.86 radiant. Okay, so now we will put better by two hair. So I divided by not. It will be it will be a sign 7.86 divided by 7.86. Okay. Please note it is radiant and it's square. So when we saw all I buy, I know that is fractional intensity. It will be 1.62 multiplied by 10 to the power negative, too. And this will be the final answer of discussion. Thank you.

This problem elastic concept of diffraction. And for the amateur dark french the position is calculated is in the situation. And if we use the small envelope approximation then we can substitute science data, viable health, so we can try it. Y equals I'm into the wavelength lambda Times telephone. The opening afterward eight. Okay, so the position of the first maximum is in between the position of the second minima and the first minimum. So the portion of the second minimize to lambda elevon and the position of the first minimize lambda telephone. So the position of the forced maximum Is 1.5 lambda telephone. Okay so from this the word of the slave bagels, 1.5 λ telephone Y van max. Okay, substitute the values so N equals 1.5. Into the equivalent is 500 nm of 500 into tenders -9 m into the Valley of L. That is 1.4 m upon the position of the first maximum. From the central maximize three or 3 two And there's -3 m. So the birth of the threat is a Cuban, 0.35 and two tenders -3 m At the width of the Slater's 0.35 mm

For the defection. Sine theta is equal to M times lamb daddy. Bye bye. Hey, is this literally? That's what we are looking for for every school, too. A musical. Zero plus minus one plus minus two word. Then why am will be pulled to l then, which is approximately equal. To think that I am is approximately to sign that him. And from a boy equation, we can substitute the early for sine theta. This will become him, Linda Help Divided by a Then why will be called to write one plus y two divided by two. This will be one plus two. Well times. Well, Linda will divided by a divided by two. This will give us three Linda. Everybody but to a yeah from here of then we can solve for a so it will be three. Linda l divide by two y What? What's up? Student Ready for Linda L. And why It will be three times of 500 dime Stint, Omar. This line 1.4 divided by two times why he's three times 10 to the power minus three nature. This gives us the word off. The slipped to be 3.50 time to our minus four. Beecher

So is this. Custody were asked to find How far is the first four? Different infringes from the central maximum fritch. So let's first finds of First Bride for confronting French Reside somewhere over here is here. Okay, so in this chapter, we know is that who taught fringes for a stock finches that nobody has the second act fringes to land over D. The central French is in between Some soy swore put five planned already or three loomed over to tea. So we have the angle Science, Ada, you wholesale under forty and we know this Saito will be the same Isa Seda That gives you the position. So ten geant seita. This seder equals X over hill and in double slit interferences. What we often do is we equate sciences or two tendencies because we know they're equal. Or like or like because for small and goes, we know there are almost equal. The reason we should try to avoid doing that is because he's single, stood interference is a lot of times the soda would do is start small angle. And Cath was tried to calculate the seed out. Double check whether it is small enough so we can just ignore attention, sailor and say it's equally sensitive. So his first playing the Firstman Science data equals thiss so Seo equals r ked Sign It got three. Linda Over Tootie and Pug is an obvious excuse me three times six twenty times ten to Z Negative kind meter over two times three parents age times tent his inactive six meter and putting us into the calculator. I get an anger or fourteen point seventeen degree. So this is. Actually, it's not a sad, small angle like this, too. It's like it's the edge of us more usually where we define small angle, we say fifteen degrees, so this is not his address. Fall on. So because of that, I will actually do treat. I would treat tension Seita as tenders say, nice stuff, science data and then we can find the distance X equals. There are times tension. Cedar equals ten meters times attention off fourteen point one seven degree, which gives us two point fact a meter. Yes, so that it will be actually quite far from was essential. Massoumeh Fridge. Except for his bride, fridge and sort of central mass, my French is going to be pretty, spread it. And also it's just you can see that humidor intimate er, like the angle Seda. It really isn't that small. So it's just one reason for single slit you. You should not be using a small angle approximation. Or at least you should be more cautious with it. And this question is an example. You think it's small, but it's not really.


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