How Many Diffraction Orders Are Visible with a 5000 Lines/cm Grating?

[clockworks204]

1. Light of wavelength 632.8nm is normally incident upon a grating of 5000 lines/cm. How many different diffraction orders can be seen in transmission?



2. m(lambda)=d(sintheta)



3. According to my text, d=1/5000lines/cm = 2x10^-6m
and sintheta= lambda/d = 632.8x10^-9/ 2x10^6 = .3164
If I take sin^-1(.3164), I get 18 degrees.
From here, I don't know what to do because the answer is that 7 beams exist, corresponding to 4 orders, and I don't know how to get to that answer!

 

[rl.bhat]

sinθ = mλ/d.

λ/d = 0.3164. sinθ cannot be more than 1. So m should be 3. Hence there are 3 beams on either side and one central beam.

 

[clockworks204]

Thanks for your reply. Although I understand what you are saying about the 3 beams on each side with one central, how do you derive that explanation from 0.3164?

 

[rl.bhat]

Thanks for your reply. Although I understand what you are saying about the 3 beams on each side with one central, how do you derive that explanation from 0.3164?

sinθ = nλ/d. if n = 3
sinθ = 3*λ/d = 3*0.3164 = 0.9492< 1. So n cannot be more than 3.

 

[clockworks204]

Thanks, I understand now.