Question

In an interference of two similar waves with equal amplitudes $A_0$ and the intensity $I_0$. Determine the net intensity at a point where the path difference between two waves is $2\lambda$.

• A. $I_0$
• B. $4I_0$
• C. $\frac{I_0}{2}$
• D. $\frac{I_0}{4}$

Answer 1

The correct option is B $4I_0$

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, $\Delta \text{x}=2\lambda$

So the phase difference is given by,

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

$\Rightarrow \varphi =\frac{2\pi }{\lambda }\times 2\lambda =4\pi$

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

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

$=I_0+I_0+2\sqrt{I_0^2}\cos 4\pi$

$\therefore I=4I_0$

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