(a)\(R=\frac{\lambda}{\Delta \lambda_{min}}=\frac{700\overset\circ A}{1}=mN=7000\)

\(N=\frac{R}{m}=\frac{7000}{1}=7000\)

\(a=\frac{2}{7000}cm\)grooves

(b)\(m \lambda=a sin \theta \approx a \theta \approx a\frac{y}{f}\)

\(m \Delta \lambda=a \frac{\Delta y}{f}\)

\(\Delta y=\frac{m f \Delta \lambda}{a}=\frac{(1)(50cm)(1*10^{-10}m)}{2/7000cm}=0.0175mm\)