In the figure below $($not to scale$),$ let $L=1\mathrm{.}20m$ and $d=0\mathrm{.}150mm$ and assume the slit system is illuminated with monochromatic $520-$nm light.

$($a$)$ Calculate the phase difference between the two wave fronts arriving at $P$ when $=0\mathrm{.}500.$ rad

$($b$)$ Calculate the phase difference between the two wave fronts arriving at $P$ when $y=5\mathrm{.}00mm.$ rad

$($c$)$ What is the value of $$ for which the phase difference is $0\mathrm{.}333$ rad?

$($d$)$ What is the value of $$ for which the path difference is $\frac{}{4}?$