(a)\(R=\frac{\lambda}{\Delta \lambda_{min}}=\frac{6563 \overset \circ A}{1.8 \overset \circ A}=mN\)

\(N=\frac{R}{m}=\frac{\frac{6564}{1.8}}{1}=3647 grooves\)

(b)\(sin \theta_b=\frac{m \lambda}{2a}\)

\(22^0 12'=22^0+12'*\frac{1^0}{60'}=22.2^0\)

\(a=\frac{m \lambda}{2 sin \theta_b}=\frac{(1)(6300 \overset \circ A)}{2 sin 22.2^0}=8.337*10^{-5}cm\)

\(\frac{1}{a}=1200 grooves/mm\)

(c)\(W_{min}=\frac{3647gr}{1200gr/mm}=3.04mm\)