# 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

Actually in real problem which I solved on a paper I wrote 1/10000 X 1/100 and converted it into right unit .