Question

Two monochromatic light waves of amplitudes $A$ and $2A$ interfering at a point, have a phase differences of ${60}^{\circ }$. The intensity of the resultant wave at that point will be proportional to

• A. $9A^2$
• B. $3A^2$
• C. $5A^2$
• D. $7A^2$

Answer 1

The correct option is D $7A^2$

The resultant amplitude is given by,

$A_R^2=A_1^2+A_2^2+2A_1{A}_2\cos \varphi$

$A_1,A_2-$ Amplitudes of the interfering waves

$\varphi$ - Phase difference between interfering waves

Resultant amplitude of the wave is given by

$A_R^2=A^2+(2A{)}^2+[2\times A\times \left(2A\right)\cos {60}^{\circ }]$

$\Rightarrow A_R^2=A^2(1+4+2)=7A^2$

We Know that, Intensity, $I\propto A^2$

$\Rightarrow I_R\propto A_R^2$

$\therefore I_R\propto 7A^2$

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