Question

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

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

Answer 1

The correct option is C $9I$ and $I$

Here, $I_1=I,I_2=4I$

The resultant intensity at a point due to superposition of waves is given by,

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

For maxima, $\cos \varphi =1$, so that,
$I_{max}=I_1+I_2+2\sqrt{I_1{I}_2}$
$=I+4I+2\sqrt{I\times 4I}$
$\therefore I_{max}=9I$

Similarly, for minima, $\cos \varphi =-1$

And, $I_{max}=I_1+I_2-2\sqrt{I_1{I}_2}$

$=I+4I-2\sqrt{I\times 4I}$
$\therefore I_{min}=I$

Hence, $\left(C\right)$ is the correct answer.