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When the rays hit the grating at an angle $\theta_i$, there is an extra contribution to the difference in path lengths. Can you calculate this extra contribution? Also, I'm not sure if your initial equation is correct. Is $\theta$ measured relative to the incident beam, rather than the normal?.Di↵raction Grating Equation with Example Problems1 1 Grating Equation In Figure 1, parallel rays of monochromatic radiation, from a single beam in the form of rays 1 and 2, are incident on a (blazed) di↵raction grating at an angle i relative to the grating normal. These rays are then di↵racted at an angle r..known as the grating equation. The equation states that a diffraction grating with spacing will deflect light at discrete angles (), dependent upon the value λ, where is the order of principal maxima. The diffracted angle, , is the output angle as measured from the surface normal of the diffraction grating..Grating lobes will occur whenever the size of individual elements in an array is equal to or greater than the wavelength, and there will be no grating lobes when element size is smaller than half a wavelength. (For element sizes between one-half and one wavelength, the generation of grating lobes will depend on the steering angle.).Real-time monitoring of railway infrastructures using fibre Bragg grating sensors. Author links open overlay panel N. Roveri A. Carcaterra A. Sestieri. Real time monitoring of railway traffic and SHM of railway infrastructures. Dynamic equation.