Homework Help: What is the light's wavelength?

1. May 23, 2012

yy205001

1. The problem statement, all variables and given/known data
A diffraction grating having 500 lines/mm diffracts visible light at 30°. What is the light's wavelength?

d = 1/500(lines/mm) = 2x10-6(m)
θ = 30° = pi/6 rad⇔
2. Relevant equations
d*sin(θm) = mλ

3. The attempt at a solution
when i rearranged the equation, i got λ = d*sin(θm)/m
And the problem was how can i find what is the order of the diffraction?
I assumed it to be the first order, so m=1, and i got the wavelength was 1000nm but the answer was 500nm, so it must be the second order, m=2. But i have no idea how to get m=2

2. May 24, 2012

cepheid

Staff Emeritus
It says the grating diffracts *visible* light. The order m = 2 is the only one for which you get an answer for lambda that is in the visible range. A wavelength of 1000 nm is too large, and the wavelengths for all orders higher than 2 are too small.

That's one way I can think of to arrive at the answer. I could also be missing something else. But for now, this is what I can come up with.