Solve Maximum Number of Fringes Observed from Laser Beam on Grating

[noobie!]

i would like to ask a que regarding physical optic,so let's nt beating abt the bush,
QUE:A laser beam is incident on a 1.50 x 10^4 grove per inch diffraction grating.The wavelength of the light produced by the laser is 6.30nm and the interference pattern is observed on a screen 2.00m from the grating.Determine maximum number of fringes that can be observed?
here goes the solution but I am nt really clear of the solution:
d sin teta = m X lamda
sin teta=m.lamda.N/l <1
m< l/2N ans is 2.69.
tis is my que,why d=l/N wat does it represents for l/N ?then why do sin teta=m.lamda.N/l <1?why?is it because of polarized light is lesser than 1 while unpolarized light bigger than 1?thanks for your help!

 

[rl.bhat]

d is distance between two successive groves, and N is the number of groves per meter.
And sin theta is always <1

 

[noobie!]

d is distance between two successive groves, and N is the number of groves per meter.
And sin theta is always <1

oh..ya,thanks a lot,1 more doubt please,what does it mean with 1st order?is that mean a pair of fringe which involves bright and dark fringe?so as the same que as above i asked,so the m value is 2.69..so there are 5 fringes detected,m i wright?2 bright fringes and 2 dark fringes and 1 center max?please tell me if I am wrong?!thanks...

 

[rl.bhat]

When you observe the diffracted along the normal to the grating you see a bright spot. When you move on either side, at a certain angle, again you see bright spots. These are called the first order spots, because the satisfy the relation d*sin(theta) = lambda. If you move still further, again you can see bright spots, which satisfy the condition d*sin(theta) = 2*lambda. These are called second order spots. And so on.

 

[noobie!]

When you observe the diffracted along the normal to the grating you see a bright spot. When you move on either side, at a certain angle, again you see bright spots. These are called the first order spots, because the satisfy the relation d*sin(theta) = lambda. If you move still further, again you can see bright spots, which satisfy the condition d*sin(theta) = 2*lambda. These are called second order spots. And so on.

then what about dark spot?is it after at certain angle u observed u saw bright spot at the same time it has dark spot?i;m so sorry for troubling you..