A) \[\frac{I}{8}\]
B) \[\frac{I}{3}\]
C) \[\frac{I}{2}\]
D) \[\frac{I}{4}\]
Correct Answer: D
Solution :
[d] Path difference of two interfering waves at P is \[\Delta x=10\lambda =60000\overset{o}{\mathop{A}}\,\] In water the wavelength of light changes to \[\lambda '=\frac{\lambda }{\mu }=\frac{6000}{4/3}=4500\overset{o}{\mathop{A}}\,\] Phase difference between waves at P is \[\lambda =\frac{2\pi }{\lambda },\,\,\Delta x=\frac{2\pi }{4500}\times 60000=\frac{80\pi }{3}=26\pi +\frac{2\pi }{3}\] Intensity at P will be \[I'=4{{I}_{0}}{{\cos }^{2}}\left( \frac{\delta }{2} \right)=4{{I}_{0}}{{\cos }^{2}}\left[ 13\pi +\frac{\pi }{3} \right]\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,I'=4{{I}_{0}}.\frac{I}{4}\] It is given that \[4I0=I\] \[\therefore \,\,\,\,\,\,\,\,\,I'=\frac{I}{4}\]
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