Question

Two coherent monochromatic light beams of intensities $ I $ and $ 9I $ are super imposed. The maximum and the minimum intensities of the resultant beam are:

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

Answer 1

Answer: (D)

The ratio of maximum to minimum intensity 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)}=\frac{{{4}^{2}}}{{{2}^{2}}} $ $ =\frac{16}{4} $