Question

For constructive interference to take place between two monochromatic light waves of wavelength $\lambda$, the path difference should be:

• A. $(2n-1)\frac{\lambda }{4}$
• B. $(2n-1)\frac{\lambda }{6}$
• C. $n\lambda$
• D. $(2n-1)\frac{\lambda }{2}$

Answer 1

The correct option is C $n\lambda$

For constructive interference the two monochromatic light waves should be in phase.

If the path difference is $\lambda$, then $\varphi$ the phase difference is $2\pi$.

Thus, for constructive interference the two waves will be in phase if $\varphi$ is a multiple of $2\pi$ i.e $2n\pi$ where n is an integer.

Thus, $2\pi$ corresponds to $n\lambda$ path difference.