Question

Two coherent light sources $A$ and $B$ are at a distance $3 \lambda$ from each other $(\lambda=$ wavelength $)$. The distance from $A$ on the $+ X$-axis at which the first constructive interference is found to be $N \lambda$. What is the value of $N$ ?

Answer 1

Let $P$ be the point on $X$-axis, where constructive interference is obtained and $AP$ be $x$.

For first constructive interference,
$BP - AP =\lambda$
Further, $\sqrt{9 \lambda^{2}+x^{2}}-x=\lambda$
$\therefore 9 \lambda^{2}+x^{2}=x^{2}+\lambda^{2}+2 x \lambda$
$x=4 \lambda$