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I am interested in doing some solar spectroscopy on my own for fun. How do I go about choosing the appropriate diffraction grating?

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There isn't a lot of engineering here. Just use a grating dense enough to give you a comfortable angle. Less dense grating (fewer lines per mm) means a more shallow angle and narrow spectrum, and that can be harder to use. Super-dense grating might be expensive and fragile. Stay somewhere in the middle - you'll have to do a few trial runs on your own, see what works for you.

I made this spectrograph for my kids, works well enough:

http://sci-toys.com/scitoys/scitoys/light/spectrograph/spectrograph.html

I used the cheap grating that they provide on their own store, 1000 lines / mm, not bad:

http://www.scitoyscatalog.com/product/DIFFRACTION.html

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