Question

Two coherent monochromatic beams of intensities $l$ and $4l$ respectively are superposed. The maximum and minimum intensities in the resulting pattern are:

• A. $5I,2I$
• B. $9I,I$
• C. $4I,3I$
• D. $5I,I$

Answer 1

The correct option is B

$9I,I$

Step 1: Given;

$$\begin{gathered} I_1=4I \\ {I}_2=I \end{gathered}$$

Step 2: Formula used;

For maximum intensity

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

For minimum intensity

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

Step 3: Find the maximum intensity;

$I_{max}={(\sqrt{4I}+\sqrt{I})}^2={(2\sqrt{I}+\sqrt{I})}^2=9I$

Step 4: Find the minimum intensity;

$I_{min}={(\sqrt{4I}-\sqrt{I})}^2={(2\sqrt{I}-\sqrt{I})}^2=(\sqrt{I}{)}^2=I$

Hence, maximum intensity is $9I$ and minimum intensity is $I$.

Thus, option B is correct.