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
B
l0
C
5l0
D
3l0

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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