Question

In the interference of two waves with identical amplitudes $A_0$ and the intensity $I_0$, the resultant intensity at a point where the path difference between two waves is $\frac{\lambda }{3}$ will be

• A. $I_0$
• B. $2I_0$
• C. $\sqrt{2}{I}_0$
• D. $\sqrt{3}{I}_0$

Answer 1

The correct option is A $I_0$

Given :

Amplitudes of two waves, $A_1=A_2=A_0$

Intensities of two waves, $I_1=I_2=I_0$

Path difference between two waves, $\Delta \text{x}=\frac{\lambda }{3}$

So the phase difference is given by,

$\varphi =\frac{2\pi }{\lambda }\times \Delta \text{x}$

$\varphi =\frac{2\pi }{\lambda }\times \frac{\lambda }{3}=\frac{2\pi }{3}$

Further, we know that the formula for resultant intensity is given by,

$I=I_1+I_2+2\sqrt{I_1{I}_2}\cos \varphi$

$=I_0+I_0+2\sqrt{I_0^2}\cos \frac{2\pi }{3}$

$\therefore I=I_0$

The resultant intensity at a point where the path difference between two waves is $\frac{\lambda }{3}\text{will be}{I}_0.$

Hence, option $\left(\text{A}\right)$ is correct.