# Two waves have a phase difference of $\pi$. and they have light intensities I and 9I. What will be the resultant intensity .

$(a)\;I \\ (b)\;10\;I \\ (c)\;3\;I \\ (d)\;4\;I$

$I'= I_1 +I_2 + 2 \sqrt {I_1 I_2 \cos \phi}$
$I_1 =I ; I_2=9I ; \phi =\pi$
$I_1 =I+9I + 2\sqrt {9I^2 \cos \pi}$
$\qquad= 10I -6I$
$\qquad= 4I$
Hence d is the correct answer.
answered Jan 24, 2014 by