Question

The condition for constructive interference in Lloyd's single mirror experiment is the path difference which is equal to

• A. $N\lambda$
• B. $(2N-1)\frac{\lambda }{2}$
• C. $(N-1)\frac{\lambda }{2}$
• D. $\frac{\lambda }{2(2N-1)}$

Answer 1

The correct option is B $(2N-1)\frac{\lambda }{2}$

A phase change of $\pi$ occurs due to reflection from a mirror.

Hence a path difference of $\lambda /2$ exists between the two sources, original source and the image of the original source.

Thus for constructive interference at any point y on screen,

$\frac{yd}{D}+\frac{\lambda }{2}=N\lambda$

Thus the path difference at any point for constructive interference must be

$\frac{yd}{D}=N\lambda -\frac{\lambda }{2}=(2N-1)\frac{\lambda }{2}$