Question

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

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

Answer 1

The correct option is D $25l$ and $l$

Given : $I_1=9l$ and $I_2=4l$

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

$I_{max}=(\sqrt{9l}+\sqrt{4l}{)}^2=$ $(3\sqrt{l}+2\sqrt{l}{)}^2=(5\sqrt{l}{)}^2=25l$

Minimum intensity $I_{min}=|\sqrt{I_1}-\sqrt{I_2}{|}^2$

$I_{min}=(\sqrt{9l}-\sqrt{4l}{)}^2=$ $(3\sqrt{l}-2\sqrt{l}{)}^2=(\sqrt{l}{)}^2=l$