For your science fair project, you need to design a diffraction grating that will disperse the visible spectrum (400-700nm) over 30 degrees in first order.
How many lines per mm does your grating need?
sin(Θ) = mλ/d
y = Ltan(Θ)
I'm pretty sure the only equation I need is the first one.
The Attempt at a Solution
I'm not really sure where to start. I tried plugging in 400 nm and 700 nm in the first equation with m =1 and Θ=30°. But I don't get the right answer with either. If I use 400 nm, I get 1250 lines/mm which is close to the answer but not exact. The answer is 1230 lines/mm but I don't know how they get that answer.