Two light waves are represented by y₁ = a sinwt and y₂ =a sin(wt +d). The phase of the resultant wave is

$I=4I_{0}co{s}^2\left(\frac{\delta }{2}\right)$

$\varphi =\frac{\delta }{2}$

$\mathrm{tan\varphi }=\frac{\mathrm{sin\theta }}{1+\mathrm{cos\theta }} \mathrm{when} \mathrm{two} \mathrm{waves} \mathrm{have} \mathrm{same} \mathrm{amplitude}$

$\mathrm{on} \mathrm{simplyfing} \mathrm{tan\varphi }=\tan \frac{\mathrm{\theta }}{2}$

so $here \theta =\delta so \varphi =\delta /2$