Question

Two coherent light sources each of wavelength $\lambda$ are separated by a distance 3$\lambda$. Find the total number of minima formed on line AB (shown in the figure) which runs from -∞ to +∞ is (Answer upto two digits after the decimal point.)

Answer 1

Lets take any general point $S$on the line $AB$.
For any position of $S$ on line $AB$; we have for$\Delta PQS:PQ+QS>PS$
Hence, $PS-QS<\; PQ$
As $PS-QS$ represents the path difference at any point $S$ on $AB$
It can never be more than PQ which is 3$\lambda$.
Now minima occur at
$\frac{\lambda }{2},\frac{3\lambda }{2},\frac{5\lambda }{2}$ only.

So, in total three minima below mid point of AB and three above above the mid point of AB can be seen.

So, total number of minima formed are 6 on the line $AB$.