(a) \(\Delta=m\lambda=2(1cm)=2*10^7 nm\)

\(\nu=1-m\frac{\Delta \lambda}{\lambda}=1-\frac{(\Delta)(\Delta \lambda)}{\lambda^2}=1-\frac{(2*10^7 nm)(0.0013nm)}{(643.847nm)^2}=0.937\)

(b) for 5cm movement

\(\Delta=m\lambda=2(5cm)=10^8 nm\)

\(\nu=1-\frac{(\Delta)(\Delta \lambda)}{\lambda^2}=1-\frac{(10^8nm)(0.0013nm)}{(643.847nm^2)}=0.686\)

(c) if \(\nu=0\)

\(\nu=1-\frac{(2d)(\Delta \lambda)}{\lambda^2}=0\)

\(d=\frac{\lambda^2}{2\Delta \lambda}=\frac{(643.847nm)^2}{2(0.0013nm)}=15.94cm\)