Question

Two coherent monochromatic light beams of intensities $4I$ and $9I$ are superimposed. The maximum and minimum possible intensities in the resulting beam are

• A. $3I$ and $2I$
• B. $9I$ and $5I$
• C. $16I$ and $3I$
• D. $25I$ and $I$

Answer 1

The correct option is D

$25I$ and $I$

Step 1: Given

Two coherent monochromatic light beams of intensities $4I$ and $9I$ are superimposed.

Step 2: Calculation of the maximum intensity

The maximum intensity can be calculated by the following formula

$I_{\max }={\left(\sqrt{I_1}+\sqrt{I_2}\right)}^2$

Here, $I_{\max }$ is the maximum intensity, $I_1$ and $I_2$ are the intensities of the light beams.

$$\begin{gathered} I_{\max }={\left(\sqrt{4I}+\sqrt{9I}\right)}^2 \\ {I}_{\max }={\left(2+3\right)}^{2}I \\ {I}_{\max }=25I \end{gathered}$$

Hence, the maximum intensity of the resulting light beam is $25I$.

Step 3: Calculation of the minimum intensity

The minimum intensity can be calculated by the following formula

$I_{\text{min}}={\left(\sqrt{I_1}-\sqrt{I_2}\right)}^2$

Here, $I_{\text{min}}$ is the minimum intensity.

$$\begin{gathered} I_{\text{min}}={\left(\sqrt{4I}-\sqrt{9I}\right)}^2 \\ {I}_{\text{min}}={\left(2-3\right)}^{2}I \\ {I}_{\text{min}}=I \end{gathered}$$

Hence, the minimum intensity of the resulting light beam is $I$.

Therefore, option (D) is correct.