Question

Two coherent monochromatic; light beams of intensities $I$ and $4I$ are superposed. Intensities at constructive and? destructive interferenc positions will be

• A. $(5 I , 3I)$
• B. $(3 I , 2I)$
• C. $(9I , I)$
• D. $(9I , 0)$

Answer 1

Answer: (C)

$(9I , I)$

Answer 2

Here, $I_1 = I, I_2 = 4l$
At constructive interference position
$I_{c} = \left(\sqrt{I_{1} } + \sqrt{I_{2}}\right)^{2}$
$\, \, \, \, = \left(\sqrt{I} + \sqrt{4I}\right)^{2} = \left(3 \sqrt{I}\right)^{2} = 9I$
At destructive interference position,
$I_{d} = \left(\sqrt{I_{1} } - \sqrt{I_{2}}\right)^{2}$
$\, \, \, \, = \left(\sqrt{I} - \sqrt{4I}\right)^{2} = \left(- \sqrt{I}\right)^{2} = I$