Number of diffracted orders produced

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A laser beam with a wavelength of 630nm is directed at a diffraction grating with 300 lines per millimeter. The angle of diffraction for the first two orders is calculated using the formula d sin(theta) = n x wavelength, yielding an angle of 22.2 degrees for the first order. For the second part, the number of diffracted orders is determined by setting theta to 90 degrees, leading to a calculation of 5.29, which differs from the book's answer. The discussion seeks clarification on these calculations and the discrepancy with the textbook. Accurate calculations are essential for understanding diffraction patterns in optics.
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Homework Statement


Hi
A liitle help will be appreciated. The question is as follows:
A laser beam of wavelength 630nm is directed normally at a diffraction grating with 300 lines per millimetre. Calculate:
a) The angle of diffraction of each of the first 2 orders
b) The number of diffracted orders produced



Homework Equations



I used the formula

d X sintheta = n x wavelength





The Attempt at a Solution


N= 300000
therefore d= 1/300000

n=2
Wavelength = 630nm

Putting the above value in I obtained 22 .2 degrees

b) For the second part, I surmised that theta = 90 degrees
Therefore,
n = d/wavelength

I obtained 5. 29. But this diifers from the books answer.

Please help!
 
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