Question

# Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible resulting intensities are :A. 5I and 0B. 5I and 3IC. 9I and ID. 9I and 3I

Hint: Take ${{I}_{1}}$ and ${{I}_{2}}$ as the two intensities of two coherent monochromatic light beams, then find out the maximum and minimum intensity by constructing a formula with the help of those two assumed variable.

If ${{I}_{1}}$ and ${{I}_{2}}$ are two intensities of two coherent monochromatic light beams, then
${{I}_{\max }}$=($\sqrt{{I_1}}$ + $\sqrt{{I_2}}$)$^{2}$
${{I}_{\min }}$=($\sqrt{{I_1}}$ - $\sqrt{{I_2}}$)$^{2}$
Now substituting the value of ${{I}_{1}}$ and ${{I}_{2}}$ with I and 4I,
Therefore, maximum intensity
${{I}_{\max }}$=($\sqrt{I}$+$\sqrt{4I}$)$^{2}$
On solving it comes,
${{I}_{\max }}$=9I
Therefore, minimum intensity,
${{I}_{\min }}$=($\sqrt{I}$-$\sqrt{4I}$) $^{2}$
On solving it comes,
${{I}_{\min }}$=I
Therefore,
Option C is the correct option.

Maximum intensity is =($\sqrt{I}$+$\sqrt{4I}$)$^{2}$
Minimum intensity is=($\sqrt{I}$-$\sqrt{4I}$)$^{2}$