What Angles Reveal Second Order Bright Fringes in Diffraction?

[Shahab Mirza]

Hi,
1. Homework Statement
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 ?

Homework Equations

From my textbook , I got this equation , d sin theta = m (λ)

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 [/B]

 

[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.

 

[Shahab Mirza]

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.

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 a lot for your kind reply .