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Question

Path difference between two waves from a coherent sources is 5 nm at a  point P. Wavelength of these waves is 100 $$\mathring { A } $$. Resultant intensity at point P if intensity of sources is $$l_0$$ and $$4l_0$$


A
Zero
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B
l0
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C
5l0
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D
3l0
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Solution

The correct option is B $$l_0$$
$$\begin{array}{l} \Delta x=5\times { 10^{ -9 } }m \\ \Delta \phi =\frac { { 2\pi  } }{ \lambda  } \Delta x \\ =\frac { { 2\pi \times 5\times { { 10 }^{ -9 } } } }{ { 100\times { { 10 }^{ -10 } } } }  \\ =\pi  \\ Now, \\ I={ I_{ 0 } }+4{ I_{ 0 } }+2\sqrt { { I_{ 0 } } } \sqrt { 4{ I_{ 0 } } } \cos  \phi  \\ =5{ I_{ 0 } }+4{ I_{ 0 } }\left[ { \cos  \pi  } \right]  \\ ={ I_{ 0 } } \\ \therefore resula\tan  t\, \, \, { { intensity } }\, ={ I_{ 0 } } \\ Hence,\, option\, \, B\, \, is\, the\, correct\, answer. \end{array}$$

Physics

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