Question

Two coherent monochromatic light beams of intensities $I$ and 9 $I$ are superimposed. The maximum and the minimum intensities of the resultant beams are

• A. 10 $I$ and zero
• B. 10 $I$ and 8 $I$
• C. 10 $I$ and 4 $I$
• D. 16 $I$ and 4 $I$

Answer 1

Answer: (D)

16 $I$ and 4 $I$

Answer 2

The ratio of maximum to minimum intensities is $\frac{{{I}_{\max }}}{{{I}_{\min }}}=\frac{{{(\sqrt{{{I}_{1}}}+\sqrt{{{I}_{2}}})}^{2}}}{{{(\sqrt{{{I}_{1}}}-\sqrt{{{I}_{2}}})}^{2}}}$ $=\frac{{{(1+3)}^{2}}}{{{(1-3)}^{2}}}=\frac{{{4}^{2}}}{{{2}^{2}}}$ $=\frac{16}{4}$