A) \[{{I}_{0}}\]
B) \[\frac{{{I}_{0}}}{4}\]
C) \[\frac{3}{4}{{I}_{0}}\]
D) v
Correct Answer: D
Solution :
[d] Path difference |
\[={{S}_{2}}P-{{S}_{1}}P\] |
\[=\sqrt{{{D}^{2}}+{{d}^{2}}}-D\] |
\[=D\left( 1+\frac{1}{2}\frac{{{d}^{2}}}{{{D}^{2}}} \right)-D\] |
\[=D\left[ 1+\frac{{{d}^{2}}}{2{{D}^{2}}}-1 \right]=\frac{{{d}^{2}}}{2D}\] |
\[\Delta x=\frac{{{d}^{2}}}{2\times 10d}=\frac{d}{20}=\frac{5\lambda }{20}=\frac{\lambda }{4}\] |
\[\Delta \,o|\,=\frac{2\pi }{\lambda }.\frac{\lambda }{4}=\frac{\lambda }{2}\] |
So, intensity at the desired point is |
\[I={{I}_{0}}{{\cos }^{2}}\frac{\phi }{2}={{I}_{0}}{{\cos }^{2}}\frac{\pi }{4}=\frac{{{I}_{0}}}{2}\] |
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