Deviation angle for 1st order diffraction (i) A diffraction grating has 560 lines per mm. Calculate the grating spacing. If the total length of the grating is 2 cm, how many lines are there? 
  
  (ii) Light of wavelength 500 nm is incident on the grating with this spacing. Calculate the deviation angle for 1st order diffraction.


I am having difficulty with the (ii) part. For my spacing I got 0.0018 mm. So, then I used 

\begin{align}
n \lambda &amp;= d \sin{\Theta} \\
\frac{n \lambda}{d} &amp;= \sin{\Theta} \\
0.27 &amp;= \sin{\Theta} \\
\Theta &amp;= \sin^{-1}{(0.27)} = 15.7^\circ
\end{align}
The grating equation you've used is correct, and in order to find the first order diffraction angle ($n = 1$) you need to use arcsine trigonometric function and carefully place data with respective units:

\begin{align}
n \lambda &amp;= d \sin{\Theta} \tag{1}\\
d &amp;= \frac{\pu{1 mm}}{N}~[\pu{mm}] \tag{2}
\end{align}

where $N$ is number of lines per unit length. Combining (1) and (2) and converting the wavelength from nm to mm:

$$\Theta = \arcsin{\left(\frac{n \lambda}{d}\right)} = \arcsin{\left(\frac{n \lambda N}{\pu{1 mm}}\right)} = \arcsin{\left(\frac{1 \cdot \pu{5e-4 mm} \cdot 560}{\pu{1 mm}}\right)} = 16.26^\circ \tag{3}$$