Two coherent point sources `S_1 and S_2` emit light of wavelength `lambda`. The separation between sources is `2lambda`. Consider a line passing through `S_2` and perpendicular to the line `S_(1)S_(2)`. What is the smallest distance on this line from `S_2` where a minimum of intensity occurs?

Options

A. `(7 lambda)/(12)`
B. `(15 lambda)/(4)`
C. `(lambda)/(2)`
D. `(3 lambda)/(4)`

Answer

A

Explanation

Path difference at `S_(2)` us `2lambda`. Therrefore for minimum intensity at P.
`S_(1)P - s_(2)P = (3 lambda)/(2)` …..(i)
or `sqrt(4 lambda^(2) + x^(2)) - x = (3 lambda)/(2)`
Solving equation, `x = (7 lambda)/(12)`