Calculating Diffraction Orders for a 513 line/mm Grating

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For a 513 line/mm diffraction grating illuminated by 567 nm light, the maximum number of diffraction orders can be calculated using the formula m = d*sin(theta)/t, where d is the grating spacing and t is the wavelength. Assuming the angle approaches 90 degrees, the maximum value for sin(theta) is 1, leading to a calculation of m = d/t. The resulting value of m is approximately 3.4, indicating that up to 3 diffraction orders can be observed. This conclusion is confirmed by the understanding that for small angles, m would also be small, reinforcing the calculation's validity. The discussion emphasizes the importance of understanding light diffraction concepts for upcoming tests.
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# of diffraction orders seen?

Homework Statement


A 513 line/mm diffraction grating is illuminated by light of wavelength 567 nm. How many diffraction orders are seen?


Homework Equations





The Attempt at a Solution


d*sin theta = mt
t = wavelength

m = d*sin theta/t
I don't have the angle so I just omitted it assuming it would be very small and I did...
m = d/t = 3.4 so 3 diffraction orders

Is this correct?
 
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Does anyone know how to do this?
 
The value of sin has to be at a maximum (ie. 1), so the angle is 90 degrees. What you did looks right. If the angle was very small, then m would also be very small.
 
Thank you so much! I have a test on Thursday and I am having a hard time understanding light!
 

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