Question

$S_1$ and $S_2$ are two coherent sources of radiations separated by a distance $100.25\lambda ,$ where $\lambda$ is the wavelength of radiation. $S_1$ leads $S_2$ in phase by $\frac{\pi }{2}.$ A and B are two points on the line joining $S_1$ and $S_2$ as shown in the figure. The ratio of amplitudes of component waves from source $S_1$ and $S_2$ at A and B are in ratio $1:2.$ The ratio of intensity at A to that of B $\left(\frac{I_A}{I_B}\right)$ is :

• A. $\infty$
• B. $\frac{1}{9}$
• C. $0$
• D. $9$

Answer 1

Answer: (B)

$\frac{1}{9}$

Given: $Phase\left(A\right)-Phase\left(B\right)=\frac{\pi }{2}$

Let $A,2A$ are the amplitudes of $S_1$ and $S_2$ respectively.

Path difference of $\frac{\lambda }{4}$ corresponds to phase difference of $\frac{\pi }{2}$.

So at $A$ there will be destructive interference and at $B$, it is constructive interference.

Let $A_1$ & $A_2$ be amplitudes at A & B respectively

$A_1=2A-A=A$ & $A_2=2A+A=3A$

$\frac{I_A}{I_B}=\frac{A_1^2}{A_2^2}=\frac{1}{9}$