Question

In the figure below, P and Q are two equally intense coherent sources emitting radiation of wavelength 20 m. The separation between P and Q is $5m$ and the phase of P is ahead of that of Q by $90°$. A, B and C are three distinct points of observation, each equidistant from the midpoint of PQ. The intensities of radiation at A, B, C will be in the ratio:

• A. $4:1:0$
• B. $2:1:0$
• C. $0:1:2$
• D. $0:1:4$

Answer 1

The correct option is B

$2:1:0$

Step 1: Draw a diagram

Step 2: Explanation

At Point B,

$∆x=\frac{\pi }{4},∆\Phi =\frac{\pi }{2}$

$$\begin{gathered} I_B=4I{\cos }^2\frac{\pi }{4} \\ {I}_B=2I \end{gathered}$$

Therefore,

$$\begin{gathered} I=A\sin \left(\omega t-kx\right) \\ I=A\sin \left[\omega t-k\left(x+\frac{\pi }{4}\right)+\frac{\pi }{2}\right] \\ I=A\sin \left[\omega t-kx-\frac{2\pi }{\lambda }\times \frac{\lambda }{4}-\frac{\pi }{2}\right] \end{gathered}$$

Where, $I$= Intensity, $A$= Amplitude, $w$= Angular velocity,= constant and x= Speed

$\left|\begin{array}{c}∆x=\frac{\lambda }{2}\\ ∆\varphi =\pi \\ I_c=O\end{array}\right|\begin{array}{c}Therefore,Aat∆x_{effective}=0\\ Therefore,I_A=4I(Same\log icaspointAbutopposite).\\ Therefore,answeris2.\end{array}$

Hence, the correct option is (B).