b
\(\phi = \frac{{2\pi }}{\lambda }(\Delta )\)

\(\lambda , {\phi _1} = 2\pi \)

\( \lambda /4, \phi_2 = \pi/2.\)

\(I = 4{I_0}{\cos ^2}\frac{\phi }{2}\)

==> \(\frac{{{I_1}}}{{{I_2}}} = \frac{{{{\cos }^2}({\varphi _1}/2)}}{{{{\cos }^2}({\phi _2}/2)}}\)

==> \(\frac{k}{{{I_2}}} = \frac{{{{\cos }^2}(2\pi /2)}}{{{{\cos }^2}\left( {\frac{{\pi /2}}{2}} \right)}} = \frac{1}{{1/2}}\)

==> \({I_2} = \frac{k}{2}.\)