Question

Two identical coherent sources placed on a diameter of a circle of radius $R$ at separation $x(<<R)$ symmetrically about the center of the circle. The sources emit identical wavelength $\lambda$ each. The number of points on the circle with maximum intensity is $(x=5\lambda )$ :

• A. $20$
• B. $22$
• C. $24$
• D. $26$

Answer 1

The correct option is A $20$


Given:
$x=5\lambda$

From given data and diagram, we observed that

At the end of vertical diameter $\text{CD}$, zeroth maxima $(\Delta x=0)$ is obtained, and at the end of horizontal diameter $\text{AB}$, $5th$ maxima $(\Delta x=5\lambda )$ is obtained. Hence, there are $4$ maxima in each quadrant.

$\therefore$ total maxima or maximum intensity $=(4\times 4)+4=20$

Hence, option $\left(\text{A}\right)$ is correct.