Question

Two coherent sources of intensities $I_{1}$ and $I_{2}$ produce an interference pattern. The maximum intensity in the interference pattern will be

• A. $I_{1}+I_{2}$
• B. $I_{1}^{2}+I_{2}^{2}$
• C. $\left(I_{1}+I_{2}\right)^{2}$
• D. $\left(\sqrt{I_{1}}+\sqrt{I_{2}}\right)^{2}$

Answer 1

Answer: (D)

Resultant intensity $I_{R}=I_{1}+I_{2}+2 \sqrt{I_{1} I_{2}} \cos \phi$
For maximum $I_{R}, \phi=0^{\circ}$
$\Rightarrow I_{R}=I_{1}+I_{2}+2 \sqrt{I_{1} I_{2}}=\left(\sqrt{I_{1}}+\sqrt{I_{2}}\right)^{2}$