In Young's double slit experiment, the central maximum is bright in the interference pattern obtained on a screen. What will happen when: (a) light…

The condition for constructive interference is: phase difference between two waves $\displaystyle =2 n \pi$. For an initial phase difference of $\displaystyle \pi$ radian, phase difference $\displaystyle =2 n \pi \pm \pi=(2 n \pm 1) \pi$

For the central maximum, $\displaystyle n=0$, hence phase difference $\displaystyle = \pm \pi$ radian.  (Alternatively: the path difference between the interfering waves will become $\displaystyle \lambda / 2$.)