b
(b)By using phase difference \(\phi = \frac{{2\pi }}{\lambda }(\Delta )\) For path difference \(\lambda\), phase difference \({\phi _1} = 2\pi \)and for path difference  \(\lambda\)/4, phase difference \(\phi\)\(_2 \)  = \(\pi\)\(/2. \)

Also by using \(I = 4{I_0}{\cos ^2}\frac{\phi }{2}\) ==> \(\frac{{{I_1}}}{{{I_2}}} = \frac{{{{\cos }^2}({\phi _1}/2)}}{{{{\cos }^2}({\phi _2}/2)}}\) ==> \(\frac{K}{{{I_2}}} = \frac{{{{\cos }^2}(2\pi /2)}}{{{{\cos }^2}\left( {\frac{{\pi /2}}{2}} \right)}} = \frac{1}{{1/2}}\) ==> \({I_2} = \frac{K}{2}.\)