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  4. Two coherent monochromatic light sources are located at two vertices of an equilateral triangle. If the intensity due to each of the sources independently is 1 Wm-2 ) at the third vertex, the resultant intensity due to both the sources at that point (i.e., at the third vertex) is: (in text Wn-2)

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Q. Two coherent monochromatic light sources are located at two vertices of an equilateral triangle. If the intensity due to each of the sources independently is 1 Wm-2 ) at the third vertex, the resultant intensity due to both the sources at that point (i.e., at the third vertex) is: $ (in\text{ }W{{n}^{-2}}) $

EAMCETEAMCET 2006Wave Optics

Solution:

$ {{I}_{1}}={{I}_{2}}=1\,W{{m}^{-2}} $ So, resultant intensity at third vertex $ I={{(\sqrt{{{I}_{1}}}+\sqrt{{{I}_{2}}})}^{2}} $ $ ={{(\sqrt{1}+\sqrt{1})}^{2}}={{(1+1)}^{2}}=4\,W{{m}^{-2}} $