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Chapter 27, Problem 25Your answer is partially correct: Try againA dififraction Pattern forms when light Passes through a single slit; The wavelength of the light i...

Question

Chapter 27, Problem 25Your answer is partially correct: Try againA dififraction Pattern forms when light Passes through a single slit; The wavelength of the light is 689 nm_ Determine the angle that locates the first dark fringe when the width of the slit is (a) 1.6 x 10-4 mand (b) 1.6 x 10-6 m_(a) NumberUnits(b) Number"Units

Chapter 27, Problem 25 Your answer is partially correct: Try again A dififraction Pattern forms when light Passes through a single slit; The wavelength of the light is 689 nm_ Determine the angle that locates the first dark fringe when the width of the slit is (a) 1.6 x 10-4 mand (b) 1.6 x 10-6 m_ (a) Number Units (b) Number" Units



Answers

A diffraction pattern forms when light passes through a single
slit. The wavelength of the light is 675 nm. Determine the angle that
locates the first dark fringe when the width of the slit is (a) $1.8 \times 10^{-4} \mathrm{m}$
and $\quad(\mathbf{b}) 1.8 \times 10^{-6} \mathrm{m}$

Okay in this question we have to find out the angle theater which look at the dark fringes. So we have given The whip is to find one multiply by 10 Then raised to the power six m. And and that position is given is um is able to and the wavelength lambda is equal to three. 430. multiply by 10 raised to the power minus nine m. Uh huh. And and that too is given us 600 multiplied by tenders for -9 meter. We know that we know that sign. I think that it will do and lend away I. D. So theater. It will to sign universe into. Yeah. Who want to apply by 430. Exponents -9 divided by D. Which is 2.1 multiply by 10 raised to the power. Uh Six. So the uh We have is 24 degree and for the prevalent and far away of land. Uh 600 I live by Tennessee. one mine -9 nine m theatre can be completed as sign Universe into to multiply by 625 x 10 days, from -9, divided by 2.1. Multiply by 10 raised to the power six, so tita is 39 degrees.

Hi, everyone. Here it is. Given the separation of second minimum from central, try to spot is 15.2 centimeter for second. Dark from simple right, finch. Oh, yeah? So why is called too early? 10 of theater. So theater will return. And worse of this is by by two. Actually 0.15 or distance of the skin from the street is but when? Five. So it is to be 2.9 directly. Yeah. Thank you. No condition for Well, I made the order and daughter pinch the sign of theaters. But, um Linda So but it will be m lambda Born signed up to M s. Two ambulances given 6. 32.8 nanometer upon Seiler 2.9 daily. So it is to be 25015 nanometer or 25 my provider. So this is the answer of a part? No, be part bit is given by V. D's Sign of potato. Let's go to Orlando. So Rita is signed and worse of I'm Linda way d. So tita ability decrease. Mhm If Babel and three decreases Mhm. Yeah. Oh, they're so thanks for watching it

Name? Single storage. Yeah. Yeah. And infraction pattern Age obtain on the screen. Oh, Mr Prince, From it. Then by the distance of a meth order, French from the center very quickly is early. Turn of the top, right. 10 of the tattoo will be by to upon end by two. So theater two will return and words of 0.152 upon to into 0.855 That is why point, Do you know a degree? So both of the design of the cheetah, it's called to I'm Linda. So the violence of, like, design of the cheetah upon them. This is given 11.2 micrometer sign off 5.8 degree upon. And that is too. So it is to me 0.469 in my crew meter or 4. 69? No, no, we do be part why destructive interference, design or theater is called to, um, London. So that authors read is universally for personal dog angle of deflection. Mhm. Yeah. If there's any bridges. Mhm. Right, then the table. Any police? Mm. So why will be greater than 15 point was interpreted. There's a thanks for

So we know that the angular separation between the bright fringes on the Brian the bright fringe in the middle is given by this equation on Does angular separation between dark fringes and the bright fringe inimitable is given by dis equation eso in the question we know the ah wavelength and we know the distance between the two slits eso we can use for the first part for part A. We want to find out what is that angle that locates the dark French for M equals zero. So I'm going to use a sign off data equal to M plus 1/2 times Lambda over deep eso to find, um, Tatum, I need to say here, Tate icicle too in verse sign of M plus 1/2 divided by d times Lambda So em is equal to zero. Lambda is equal to 529 a meter, and D is equal to, um 1.4 times 10 to the minus six. So data would be equal to invest Sign Uh uh. 520 divided by two times 1.4 times 10 to the minus six. So, at the same time, This is not a 529 immunity. I multiplied by 10 to the minus nine to convert it to meet her. And then from here, we can get Tate out to be equal to 10 point seven degrees. Uh, for the next part, we want to find the angle of the bright fringe for em equal one eso Because this is a bright fringe. I'm going to use this equation. So here I say, sign up. Potato is equal to, uh, m lambda over D. So Tate A is a quality use in versus sign of m lambda over D. So if every substitute, all the values we get Scient, Ada, we get take bicycle too. Sine inverse ah of one times 520 times 10 to the minus nine. Divided by 1.4 times 10 to the minus six. And from here, we get data to be to any one point eight degrees for the next part of you want to find? Ah, the angle off the dark friend for M equals one. So again, Tater is a call to sign in verse off M plus 1/2 times. Lambda over. Dean and this is a call to ah sine inverse of 11 plus 1/2. Ah, three over to multiply by 520 times talk attend to the minus nine, divided by 1.4 times 10 to the minus six. And then this is equal to 33 point um 80 six agrees and then the last part. We want to find the angle off the bright French for m equals to So Tate A is ah sign converse of in Lambda over d on because any stewardesses sense sine inverse off to times 520 times 10 to the minus nine. Divided by 1.4 times 10 to the minus six. Andi From here Tater is equal to 47 point 97 vigorous.


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