What is the light's wavelength?

[yy205001]

Homework Statement

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⇔

Homework Equations

d*sin(θ_m) = mλ

The Attempt at a Solution

when i rearranged the equation, i got λ = d*sin(θ_m)/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

 

[cepheid]

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.