Question

Two identical coherent sources are placed on a diameter of a circle of radius R at a separation d (d << R, d >> $\lambda$) symmetrically about the centre of the circle. The sources emit identical wavelength $\lambda$. The number of the points on the circle with maximum intensity is

• A. $\frac{2d}{\lambda }+1$
• B. $\frac{4d}{\lambda }$
• C. $\frac{4d}{\lambda }-2$
• D. $\frac{4d}{\lambda }+2$

Answer 1

The correct option is B $\frac{4d}{\lambda }$

For maxima $d\sin \theta =n\lambda$

On circle, for $-\frac{\pi }{2}\le \theta \le \frac{\pi }{2}\Rightarrow n=\frac{2d}{\lambda }+1$

for $\frac{\pi }{2}<\theta <-\frac{\pi }{2}\Rightarrow n=\frac{2d}{\lambda }-1$

Total number of maxima $n=\frac{4d}{\lambda }$