Question

$S_1$ and $S_2$ are the two coherent point sources of light located in the xy-plane at points (0,0) and (0,3$\lambda$) respectively. Here $\lambda$ is the wavelength of light. At which one of the following points (given as coordinates), the intensity of interference will be maximum?

• A. $(3\lambda ,0)$
• B. $(4\lambda ,0)$
• C. $(5\lambda /4,0)$
• D. $(2\lambda /3,0)$

Answer 1

The correct option is B $(4\lambda ,0)$

A point P will have maximum intensity is path difference between the light reaching via path 1 and 2 is equal to $\lambda$

Path difference between the light $\Delta x=S_{2}P-S_{1}P=\sqrt{x^2+9{\lambda }^2}-x$

For maximum intensity at P, $\sqrt{x^2+9{\lambda }^2}-x=\lambda$

OR $\sqrt{x^2+9{\lambda }^2}=\lambda +x$

Squaring both sides, we get $x^2+9{\lambda }^2=x^2+{\lambda }^2+2x\lambda$

OR $+9{\lambda }^2-{\lambda }^2=2x\lambda$

$⟹$ $x=\frac{8{\lambda }^2}{2\lambda }=4\lambda$

Hence the point P must be $(4\lambda ,0)$.