diffraction grating problem

[Sarahisme]

hey i have a question about this question ....

 

ok so for interference maxima the equation is

 

[math] dsin \theta_m = m \lambda [/math] , where m = 0,1,2,...

 

now for the first grating (4000 lines/cm) and the red wavelength:

 

[math] \theta = sin^{-1}(\frac{m \lambda}{d}) [/math]

 

now my question is can i let m be anything i like or whats the deal? because wouldn't there be multiple (theoretically infinite amount) angles that construct interference could happen at?

 

 

-Sarah

[swansont]

hey i have a question about this question ....

 

ok so for interference maxima the equation is

 

[math] dsin \theta_m = m \lambda [/math] ' date=' where m = 0,1,2,...

 

now for the first grating (4000 lines/cm) and the red wavelength:

 

[math'] \theta = sin^{-1}(\frac{m \lambda}{d}) [/math]

 

now my question is can i let m be anything i like or whats the deal? because wouldn't there be multiple (theoretically infinite amount) angles that construct interference could happen at?

 

 

-Sarah

 

Yes, m can be anything as long as [math] \theta < 90[/math] However, the intensity drops off for higher dffraction angles, so in practice you can't always see them.

[Sarahisme]

so i assume the correct answer to this question would not really involve plugging in numbers then? or do you just do it for m=1 or something?

 

well the thing is in my textbook, there is a similar question, which just does it for m = 1, but isnt that not enitirely correcct, because it could be done for m =2, m=3,...etc.

 

???

 

the reason i ask is because well, since you are given numerical values then shouldn't i be producing a numerical answer?

[swansont]

so i assume the correct answer to this question would not really involve plugging in numbers then? or do you just do it for m=1 or something?

 

well the thing is in my textbook' date=' there is a similar question, which just does it for m = 1, but isnt that not enitirely correcct, because it could be done for m =2, m=3,...etc.

 

???

 

the reason i ask is because well, since you are given numerical values then shouldn't i be producing a numerical answer?[/quote']

 

Often you just need to find the first-order maximum or minimum. Depends on the question.

[Sarahisme]

ok yeah, so in terms of this question do you think it wants an algebraic or a numerical answer? or both? because i think its a bit unclear

[swansont]

Since they gave you actual numbers, I think they want a numerical answer. The algebraic answer will be included in the work you do, anyway.

[Sarahisme]

hmm yeah ok, i'll probably just give the first-order maxima then, because as you say, experimentally thats usually the most useful (easy to find) one.

 

Thanks for all you help swansont!