Maximum lines per meter for diffraction grating with 4 bright fringes per side

[dewdrop714]

1. Homework Statement

a) Exactly 4 bright fringes are seen on either side of the central maximum when a diffraction grating is illuminated with yellow-green light of a wavelength of 570 nm. What is the maximum number of lines/meter for the grating?


2. Homework Equations

sin(theta) = m(wavelength) / d

so solving for d = m(wavelength) / sin(theta)


3. The Attempt at a Solution

I want to find the max number of lines/ meter for the grating
so d= ? m/line
m = 0 because the question says central maximum
wavelength is given to you and in meters it is 570*10^-9 m

***what i don't understand is how do you find the angle Theta? Does it have to do with the "4 bright fringes" part of the question? And does that mean m=4?

because after finding the angle Theta i would be able to solve for d = m(wavelength) / sin(theta) and get an answer. Then I would do 1/answer to get the final answer in lines/m.

 

[Redbelly98]

1. Homework Statement

a) Exactly 4 bright fringes are seen on either side of the central maximum when a diffraction grating is illuminated with yellow-green light of a wavelength of 570 nm. What is the maximum number of lines/meter for the grating?2. Homework Equations

sin(theta) = m(wavelength) / d

so solving for d = m(wavelength) / sin(theta)3. The Attempt at a Solution

I want to find the max number of lines/ meter for the grating
so d= ? m/line
m = 0 because the question says central maximum
wavelength is given to you and in meters it is 570*10^-9 m

***what i don't understand is how do you find the angle Theta? Does it have to do with the "4 bright fringes" part of the question? And does that mean m=4?

Yes! Also, what is the largest angle you could have?

... because after finding the angle Theta i would be able to solve for d = m(wavelength) / sin(theta) and get an answer. Then I would do 1/answer to get the final answer in lines/m.

Yes, that's the idea.

 

[dewdrop714]

so m = 4? or m = 0? and is the largest angle you can have 180 degrees? I am still very confused on this question...

 

[Redbelly98]

m = 4 for the fourth fringe from the the central maximum.

Hope this picture shows you what is going on. The m=4 diffracted beams are shown in green. How large can the angle θ be, and still have that m=4 beam (the green beam to the left) be visible?

 

[rl.bhat]

so m = 4? or m = 0? and is the largest angle you can have 180 degrees? I am still very confused on this question...

Yes. In that 8 bright fringes are there. All of them are equally spaced. So what will be the angular separation of the first bright fringe from the central fringe?

 

[dewdrop714]

is the angle 90? so then sin of 90 = 1?

 

[Redbelly98]

Yes. Now you can do what you said before:

... after finding the angle Theta i would be able to solve for d = m(wavelength) / sin(theta) and get an answer. Then I would do 1/answer to get the final answer in lines/m.

 

[dewdrop714]

thank you so much! =]

 

[Sirenalupa]

I have the same problem but I can not understand the communication between the two of you. M=4 correct? but why would the angle be 90 and not 45?

 

[Redbelly98]

Welcome to PF

Yes, M=4.

In the figure in post #4: We're talking about the angle between the central, vertical green ray and either of the other green rays. Is it not clear that angle could be more than 45? (It's roughly 80 in the figure).