Question

Two point sources separated by $2.0 \,m$ are radiating in phase with $\lambda=0.50 \,m$. A detector moves in a circular path around the two sources in a plane containing them. How many maxima are detected?

• A. 16
• B. 20
• C. 24
• D. 32

Answer 1

Answer: (A)

Condition for maxima is
$d \sin \theta=n \lambda$
$\sin \theta=\frac{n \lambda}{d}=n\left(\frac{0.50}{2.0}\right)=0.25\, n$
As $\sin \theta$ lies between $-1$ and $1$ , so we wish to find all values of $n$ for which
$|0.25 n| \leq 1$
These values are $-4,-3,-2,-1,0,+1,+2,+3,+4$. For each of these, there are two different values of $\theta$ except for $-4$ and $+4$. A single value of $\theta,-90^{\circ}$ and $+90^{\circ}$, is associated with $n=-4$ and $n=+4$, respectively. Thus, there are $16$ different angles in all and therefore $16$ maxima.