How do I calculate how many orders of diffraction are visible if I have wavelength and grating?

Question

Please help. many thanks

Answer 1

You also need to know the angle of incidence. The fundamental equation (ref.) is
sin(alpha) + sin(beta) = 10^-6 * k * n * lambda, where
alpha is angle of incidence
beta is angle of diffraction
k is order of diffraction
n is groove density, lines/millimeter
lambda is wavelength in nanometers
With a given alpha, k, n and lambda, if you solve for beta it shouldn't be too close to 90 deg or it won't show up well. A coarser grating (smaller n) will help make higher orders (larger k) accessible.