Question

Figure shows two coherent microwave source $S_{1}$ and $S_{2}$ emitting waves of wavelength $\lambda$ and separated by a distance $3 \lambda$. For $\lambda < < D$ and $y \neq 0$, the minimum value of $y$ for point $P$ to be an intensity maximum is $\frac{\sqrt{m} D}{n}$. Determine the value of $m+n$, if $m$ and $n$ are coprime numbers.

Answer 1

Path difference $=3 \lambda \cos \theta=2 \lambda$
$ \Rightarrow \cos \theta=2 / 3$
$y=D \tan \theta=\frac{D \sqrt{5}}{2}$
$ \Rightarrow m+n=5+2=7$