Diffraction Grating: Questions & Answers

[_Mayday_]

I've been reading into diffraction grating recently, and have a few questions to ask. Firstly here is a diagram to help explain what I am on about.

http://img411.imageshack.us/img411/3972/gratingey6.png

Ok, so here is a simple diagram. If I was using a sodium lamp to shine onto the grating, it would project something similar to this, just I forgot to put the gaps in.

Firstly Am i correct in saying, in terms of collecting the data from this, that I would measure the angle from m=0 for each different colour, and the actual colour itself?

Secondly After having taken these reading, how are they relevant to their frequency? I would use the formula $$n \lambda= d \sin \theta$$ , lamba being the frequency so that is what I am after, sin theeta is the angle that I have measured, but what would "d" and "n" represent?

Thirdly What type of conclusion am I likely to draw from such results? Where would I expect higher frequencies and lower ones? And why would they be there?


I hope, this is clear enough as I have trouble explaining what I actually mean! =] Thanks.

 

[dlgoff]

m is the order of the diffraction pattern (this is your n). d is the groove period.

Look at the http://en.wikipedia.org/wiki/Diffraction_grating" on this wikipedia page.

 

[_Mayday_]

m is the order of the diffraction pattern (this is your n). d is the groove period.

Look at the http://en.wikipedia.org/wiki/Diffraction_grating" on this wikipedia page.

Ah, thanks yeh, so my $$m$$ is the $$n$$ in the formula.

On the topic of grooves I followed your link, but failed to understand what they had to say on grooves "The grating equation shows that the angles of the diffracted orders only depend on the grooves' period, and not on their shape. By controlling the cross-sectional profile of the grooves, it is possible to concentrate most of the diffracted energy in a particular order for a given wavelength."

Is there a simpler explanation of what they are? And how to measure them?

 

[dlgoff]

d is the distance between the groves.

 

[_Mayday_]

^ What are the grooves? Is it the spaces between the projected light segments on the wall? What are they measured in?

 

[dlgoff]

Do you know the double slit diffraction experiment? Where you have 2 slits separated by a small distance?

Now a gratting is like this with multiple slits (groves) separated by a distance of d. Usually you measure the slit distance by stating the number of lines/distance.

If you read further of Fabrication in the above link, I think you'll understand.

 

[_Mayday_]

Ok, so then it is the distance in which the slits in the grating are spaced? So througout the experiment "d" will actually be constant?

 

[dlgoff]

"So througout the experiment "d" will actually be constant?"

yes

 

[_Mayday_]

I think I have grasped the overall idea of the experiment now. Thank you, I know what I am looking for and how to put that into the formula to get a wavelength. What would one expect in terms of how the colours would arange themselves? I know that different colours have different frequencies, but how owuld they arrange themselves? And why?

Thanks for all your help so far, I think I'm getting it now.

 

[dlgoff]

The larger the wavelength, the greater the diffraction angle.

"In the first positive order (m = +1), colors with increasing wavelengths (from blue to red) are diffracted at increasing angles."

 

[_Mayday_]

Thanks dlgoff for all you help I understand it now. =]