A light is shone through a diffraction grating of slit spacing 4.5x10^5 lines per metre. The incident wavelength is 650nm. Find the angle produced by the incident light and the 2nd order maximum.

In the question you are given the slit spacing of the diffraction grate. To find the fringe spacing of this grate you can use d=1/N where N is the slits per metre. In this question this would be 1/4.5x10^5 = d = 2x10^-6 m. To find the angle provided by the second order maximum, rearrange the equation nλ=dsinθ to make sinθ the subject.This would then become nλ/d = sinθ.To find sinθ, sub in the values given to you in the question; i.e. n=2, λ=650nm and d=2x10^-6 m.This gives sinθ=0.65.Use your calculator to find sin^-1(0.65) to find θ=40.5°.