Question

Two identical coherent sources of wavelength $\lambda$ are placed at $(100\lambda ,0)$ and $(-50\lambda ,0)$ respectively. A detector moves slowly from the origin to $(50\lambda ,0)$ along x-axis. The number of maxima and minima detected are, respectively [include origin and $(50\lambda ,0)$]

• A. $51$ and $50$
• B. $101$ and $100$
• C. $49$ and $50$
• D. $50$ and $49$

Answer 1

The correct option is B $101$ and $100$

In a distance of $50\lambda$ only $50$ waves can accommodate at any instant. Each wave on interfering produces either two maxima or two minima at an instant.

Therefore for $50$ waves, $100$ number of maxima and $100$ would be detected without including end points. Including end points there are total of $102$ maxima and $100$ minima.

But at $(25\lambda ,0)$, which is at the middle of the two source, central maxima occurs, resulting in one less maxima detected as there is no minima to distinguish it.

So total of $101$ maxima and $100$ minima.