Question

The central fringe in the interference pattern obtained in Young's double slit experiment will be a dark fringe when the phase difference between the waves from the two slits is

• A. $0$
• B. $\frac{\pi }{2}$
• C. $\pi$
• D. $\frac{\pi }{3}$

Answer 1

Answer: (C)

When the central fringe in the interference pattern in YDSE be a dark fringe, then path difference, will be $\frac{\lambda }{2}$.
i.e., $\Delta x=\frac{\lambda }{2}$
$\therefore$ Phase difference,
$\Delta \phi =\frac{2\pi }{\lambda }\times \Delta x$
$=\frac{2\pi }{\lambda }\times \frac{\lambda }{2}=\pi$