Diffraction Gratings — Question 6

Question 6

Oblique incidence changes the asymmetric order range

Use the transmission-grating convention $d(\sin\theta-\sin\alpha)=m\lambda$. Let $d=2.00\,\mu\mathrm m$, $\lambda=500\,\mathrm{nm}$, and $\sin\alpha=0.250$. Count only directions with $|\theta|<90^\circ$.

1. Find the order along the grating normal and the direction of order zero.

2. List the complete set of forward propagating orders and identify the excluded grazing orders.

Question 6 - Solution

Oblique incidence changes the asymmetric order range

(a) Method and calculation

$$\boxed{\sin\theta_m=0.250+0.250m}.$$$$\theta=0\Longrightarrow\boxed{m=-1};\quad m=0\Longrightarrow\boxed{\theta_0=\alpha=14.4775^\circ}.$$

(b) Interpretation and further calculation

$$-1<0.25(1+m)<1\Longrightarrow-5<m<3\Longrightarrow\boxed{m=-4,-3,-2,-1,0,1,2}.$$$$\boxed{m=-5,3\ \text{are grazing and excluded}}.$$

Physical check

Order zero follows the incident propagation direction; it need not coincide with the surface normal.