Calculating Diffraction Orders for a 513 line/mm Grating

[BuBbLeS01]

# 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?

 

[BuBbLeS01]

Does anyone know how to do this?

 

[Snazzy]

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.

 

[BuBbLeS01]

Thank you so much! I have a test on Thursday and I am having a hard time understanding light!