Homework Help: Diffraction Grating Problem ?

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1. May 17, 2015

Shahab Mirza

Hi,
1. The problem statement, all variables and given/known data
Q : A diffraction grating with 10000 lines per CM is illuminated by yellow light of wavelength 589 nm, At what angles is the 2nd order bright fringes seen ?

2. Relevant equations
From my text book , I got this equation , d sin theta = m (λ)

3. The attempt at a solution
Ok so what I did was that I plugged values properly , i.e
sin theta = mλ/d
For second order , m=2 so,
= (2) (589 X 10nm) / (1/10000 X 1/ 100)

and the answer is 1.178 , but out teacher said that this number is larger than 1 and so sin theta does not represent any rational angle , so tell me that how to know that sin theta in this case "1.178" does not represent any rational number , please help me out with this , Thanks

2. May 17, 2015

ehild

What does 589x10 nm mean? You have to substitute the wavelength in meters.
The value you got for sin(theta) is correct, perhaps the grating constant is 1000/cm instead of 10000/cm. The grating constants are usually in the range of micrometers.
Your teacher is right, in case of such fine grating, the second maximum does not appear.

3. May 17, 2015

Shahab Mirza

Thanks for reply Sir ,
Actually in real problem which I solved on a paper I wrote 1/10000 X 1/100 and converted it into right unit .
Thanks alot for your kind reply .

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