Finding order of diffraction given angle and wavelength

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Homework Help Overview

The discussion revolves around calculating the grating constant, d, using the equation d = mλ / sinθ, where the angle θ is given as 172.01167 degrees and the wavelength λ is 447.2 nanometers. Participants explore the implications of the angle exceeding 90 degrees and the context of the measurements taken during a lab involving Helium in a spectrometer.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants question the definition of the angle and its implications, particularly its value being greater than 90 degrees. There is discussion about the completeness of the problem statement and whether additional context about the diffraction grating is necessary. The original poster expresses uncertainty about determining the order of diffraction and how to identify where one order ends and another begins.

Discussion Status

Some participants have offered insights regarding the nature of the measurements and the identification of the first order of diffraction. There is an ongoing exploration of how to recognize patterns in the diffraction results to distinguish between different orders.

Contextual Notes

The original poster notes that the measurements are based on real-world values from a lab experiment, and there is mention of the light becoming dimmer as measurements progressed. This context may influence the interpretation of the diffraction pattern.

AardeeHar
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Homework Statement


Calculate the grating constant, d, given that theta = 172.01167 degrees, and that lambda = 447.2 nanometers.

2. Homework Equations

d = mλ / sinθ

where m is an integer that refers to the order of diffraction
where λ is the wavelength
where d is the spacing between two slits
where θ is the angle observed

The Attempt at a Solution


I understand the equation, but given the fact I have two variables (being m and d) I am unsure of how to solve. How do I determine the order of diffraction?
 
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How is that angle defined? That it's greater than 90° seems strange to me.
 
I'm sorry, I'm not exactly sure what you mean. The central angle is 180 degrees.
 
AardeeHar said:
I'm sorry, I'm not exactly sure what you mean. The central angle is 180 degrees.
Okay, I believe that answers my question. I was wondering whether the grating was being used in transmission or reflection mode, and how the angle was being specified. So the angle between the projected incident ray and deflected ray is actually 180° - θ.

What is the significance of the variable name sigma? Is there a reason why you've named it sigma rather than lambda?
 
Sorry, that was my mistake with the name of the greek letter. I've changed it in the original question.
 
AardeeHar said:
Sorry, that was my mistake with the name of the greek letter. I've changed it in the original question.
Okay, understood. (FYI, you can access a menu of special characters like the Greek letters if you click on the ##\Sigma## icon in the edit panel top bar).

Now I understand your dilemma. Is the problem statement complete in and of itself, or was it posed in some context where we might know something else about the diffraction grating or what was measured?
 
It was part of a lab. So, all these are "real world" values. The only other information I can see that may be relevant is that the light (we were looking at Helium in a spectrometer) became dimmer as we moved through each individual sample. Beyond that, I don't really have much else to work with.
 
Okay, since you made the observation you would have noted if there were repeating units of the diffraction pattern before the one you measured the line's angle in, right? If there were no "earlier" orders in evidence then this must be the first order.
 
gneill said:
Okay, since you made the observation you would have noted if there were repeating units of the diffraction pattern before the one you measured the line's angle in, right? If there were no "earlier" orders in evidence then this must be the first order.

Okay, I believe I understand what you are saying. Since this is my "first" measurement (which it is), it must be order one. That makes sense. I have six remaining measurements (7 total). How can one determine where order "one" ends, and order "two" begins? I very much appreciate your help by the way. :)
 
  • #10
AardeeHar said:
Okay, I believe I understand what you are saying. Since this is my "first" measurement (which it is), it must be order one. That makes sense. I have six remaining measurements (7 total). How can one determine where order "one" ends, and order "two" begins? I very much appreciate your help by the way. :)
It's a matter of pattern recognition. The pattern of lines should repeat (color and relative spacing) for each order.
 
  • #11
Oh, I see! I didn't realize that. Thank you so much, now I understand.
 

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