Answer
$160^{\circ}$
Work Step by Step
$\text{Phase difference}=\frac{2\pi}{\lambda}\text{(Path difference)}$
The path difference between the Huygens wavelets arriving at point P from the top and midpoint of the slit is given by
$\text{Path difference}=\frac{a}{2}\sin\theta$
where, $a$ is slit width, $\theta$ is the location of point P from the central axis of the slit
Substituting the given values, we have
$\text{Path difference}=\frac{0.10\;mm}{2}\sin30^{\circ}=0.025\;mm$
or, $\text{Path difference}=2.5\times10^{-5}\;m$
Therefore,
$\text{Phase difference}=\frac{2\pi}{589\times 10^{-9}}\times 2.5\times10^{-5}$
or, $\text{Phase difference}=84.8896\pi$
Therefore final phase difference is
$84.8896\pi-84\pi=0.8896\pi\approx 160^{\circ}$
