Maxima of Diffraction Grating with 300 Lines/mm and Wavelength of 450 nm

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Homework Help Overview

The problem involves determining the number of orders of diffraction maxima produced by a grating with 300 lines per millimeter when illuminated by light of wavelength 450 nm. The context is rooted in the principles of diffraction and the application of the grating equation.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to calculate the maximum order of diffraction using the grating equation but expresses confusion regarding the correct answer. Other participants question the nature of maxima and minima in relation to the grating's center and the possible values for the order of maxima.

Discussion Status

Participants are actively exploring the problem, with some providing clarifications about the nature of maxima and the values that the order variable can take. There is no explicit consensus on the correct number of maxima, but guidance has been offered regarding the interpretation of the grating's behavior.

Contextual Notes

There is a noted discrepancy between the original poster's calculation and the expected answer, indicating potential misunderstandings about the application of the grating equation or the interpretation of the results. The discussion includes questions about the symmetry of the diffraction pattern and the definition of the order of maxima.

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Homework Statement



Light of wavelength 450 nm is incident normally on a grating with 300 lines per millimeter. How many orders of diffraction maxima can be obtained?



Homework Equations


d sin(theta) = n(lambda)

The Attempt at a Solution


300 lines per millimeter is 3.33 x 10^-6. And 450 nm should be 4.5 x 10^ -7 m.
This is my equation:
3.33 x 10^-6 sin 90 = n (4.5 x 10^ -7)
I get n= 7.4 = 7
The correct answer is 15. But i just can't get this answer. =( Can someone please guide me?
 
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What is in the middle point, just opposite to the centre of the grating, minimum or maximum? And are maxima at one side only? What values can m have?

ehild
 
Does that mean there are two maxima for each order?
 
ehild said:
What is in the middle point, just opposite to the centre of the grating, minimum or maximum? And are maxima at one side only? What values can m have?

ehild

Maxima are at both sides. But i still don't know how to get values of m.
 
Can you please give some more hints
 
m is integer, including negative numbers and zero. So the farthest maxima are either at 90°or -90°.

ehild
 

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