Question

In a Young's double-slit interference experiment using a yellow light of wavelength $\lambda$, with the slits labelled $S_1$ and $S_2$. If $P$ is the centre of a dark fringe on the screen on which the resulting diffraction pattern is projected, Find out the equations relating $S_{1}P$ and $S_{2}P$ which could be true?

• A. $S_{1}P-S_{2}P=\frac{1}{2\lambda }$
• B. $S_{1}P-S_{2}P=\lambda$
• C. $S_{1}P-S_{2}P=2\lambda$
• D. $S_{1}P-S_{2}P=3\lambda$
• E. $S_{1}P=S_{2}P$

Answer 1

The correct option is A $S_{1}P-S_{2}P=\frac{1}{2\lambda }$

A dark fringe is formed due to destructive interference of waves from the two slits. Before entering the slits, the light was in-phase. After transversing different distances, the light from the sources must go out of phase to cause a dark fringe.
Thus $S_{1}P-S_{2}P=(n+\frac{1}{2})\lambda$