A diffraction grating is designed to have the $n-$order maximum at angular position $,$ measured from the central maximum, for light with a wavelength of $.$

Question $13$

$5$ pts

Given that $n=3,=15\mathrm{.}8$ degrees, and $=680nm,$ what is the ruling constant $($number of lines per length$)$ of the grating?

Enter your answer in units of lines$-$per$-$micrometer. For example, if your calculations produce a value of $1\mathrm{.}23{10}^5$ lines $\frac{?}{m},$ first convert units to $1\mathrm{.}23{10}^5$ lines $\frac{?}{({10}^6(m))}$ or $0\mathrm{.}123$ lines $\frac{?}{m},$ then enter your answer as $0\mathrm{.}123.$

Question $14$

$5$ pts

Again, a diffraction grating is chosen so that $n=4$ and $=10\mathrm{.}7$ degrees when $=445nm.$ If another light with ${}_2=686nm$ is shined on this same grating, what is the angular position ${}_2($from the central maximum$)$ of the second$-$order maximum for this new light?

Enter your answer in degrees. For example, if your calculations produce a value of $12\mathrm{.}3,$ enter your answer as $12\mathrm{.}3.$