Finding order of diffraction given angle and wavelength

[AardeeHar]

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?

 

[gneill]

How is that angle defined? That it's greater than 90° seems strange to me.

 

[AardeeHar]

I'm sorry, I'm not exactly sure what you mean. The central angle is 180 degrees.

 

[gneill]

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?

 

[AardeeHar]

Sorry, that was my mistake with the name of the greek letter. I've changed it in the original question.

 

[gneill]

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?

 

[AardeeHar]

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.

 

[gneill]

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.

 

[AardeeHar]

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. :)

 

[gneill]

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.

 

[AardeeHar]

Oh, I see! I didn't realize that. Thank you so much, now I understand.