Explanation:
For net intensity \(I = 4{I_0}{\cos ^2}\frac{\phi }{2}\)
For the first case,
\(\because \left( {\phi = \frac{{2\pi }}{\lambda } \times \lambda } \right)\)
\(K = 4{I_0}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\)
For the second case \(K' = 4{I_0}{\cos ^2}\left( {\frac{{\pi /2}}{2}} \right)\left( {\phi = \frac{{2\pi }}{\lambda } \times \frac{\lambda }{4}} \right)\)
\(K'{\text{ }} = {\text{ }}2{I_0}{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \,\,\,(2)\)
From Eqs. (1) and (2), we get
\(K' = \frac{K}{2}\)