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 $y\ne 0$, 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

Answer: 7

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