Diffraction Grating

You are given enough information to calculate d, and you are given the values of $\lambda$ and m. You will have to find the arcsin of a number to find $\theta$ .

First find d.

Rearrange the equation for constructive interference conditions for a diffraction grating, and substitute the known values.

$$\begin{array}{ccc}\hfill d\sin \theta & \hfill =\hfill & m\lambda \hfill \\ \hfill \theta & \hfill =\hfill & {\text{sin}}^{-1}\frac{m\lambda }{d}\hfill \\ \hfill & \hfill =\hfill & {\text{sin}}^{-1}\left(\frac{(1)(520)}{\mathrm{5,000}}\right)\hfill \\ \hfill & \hfill =\hfill & 5.97\hfill \end{array}$$