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

Question

Two coherent monochromatic light beams of intensities I and 4I are superposed- The maximum and minimum possible resulting intensities are -5I and 05I and 3I9I and I9I and 3I

Toppr Admin · Accepted Answer

Maximum intensity- Imax-x221A-I1-x221A-I2-2-x221A-I-x221A-4I-2-9IMinimum intensity Imin-x221A-I1-x2212-x221A-I2-2-x221A-I-x2212-x221A-4I-2-I

Two coherent monochromatic light beams of intensities $I$ and $4 I$ are superposed. The maximum and minimum possible resulting intensities are :
$5 I$ and $0$
$5 I$ and $3 I$
$9 I$ and $I$
$9 I$ and $3 I$

Maximum intensity, $I_{m a x} = (\sqrt{I_{1}} + \sqrt{I_{2}})^{2}$
$= (\sqrt{I} + \sqrt{4 I})^{2}$
$= 9 I$
Minimum intensity $I_{m i n} = (\sqrt{I_{1}} - \sqrt{I_{2}})^{2}$
$(\sqrt{I} - \sqrt{4 I})^{2}$
$= I$

Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible resulting intensities are :5I and 05I and 3I9I and I9I and 3I

Maximum intensity, Imax=(√I1+√I2)2=(√I+√4I)2=9IMinimum intensity Imin=(√I1−√I2)2(√I−√4I)2=I

Two coherent monochromatic light beams of intensities $I$ and $4 I$ are superposed. The maximum and minimum possible resulting intensities are :
$5 I$ and $0$
$5 I$ and $3 I$
$9 I$ and $I$
$9 I$ and $3 I$

Maximum intensity, $I_{m a x} = (\sqrt{I_{1}} + \sqrt{I_{2}})^{2}$
$= (\sqrt{I} + \sqrt{4 I})^{2}$
$= 9 I$
Minimum intensity $I_{m i n} = (\sqrt{I_{1}} - \sqrt{I_{2}})^{2}$
$(\sqrt{I} - \sqrt{4 I})^{2}$
$= I$