How many orders of diffraction are visible and why?
Let's consider the next problem as an example: how many orders of diffraction will be visible if light of wavelength 500nm falls on a grating with 600 000 lines per meter? Another way to pose this question is: how many maximums do you see between theta=0 and theta=90 degrees? Consider that for a maximum to appear on the wall or the screen in front of the grating the angle theta can never be more than 90 degrees.
n = d·sin(theta) / λ & lambda; = 500nm = 5 X 10^(-7)m d = 6 X 10^5 per meter = 1 ÷ 6 X 10^5 = 16.7 X 10^(-7)m n = 16.7 X 10^(-7) X sin(pi/2) ÷ 5 X 10^(-7) = 3.34
So, there will be 3 orders of diffraction visible.