A) \[\mu =\frac{5}{2}\,\,if\,\,\lambda =2t\]
B) \[\mu =\frac{5}{3}\,\,if\,\,\lambda =t\]
C) \[\mu =\frac{5}{3}\,\,if\,\,\lambda =3t\]
D) \[\mu =\frac{4}{3}for\,\,any\,\,value\,\,of\,\,\lambda \]
Correct Answer: B
Solution :
[B]As intensity decrease by 75% i.e. intensity is 25% of max intensity |
i.e. I at center of screen \[=\frac{4{{I}_{0}}}{4}={{I}_{0}}\] |
\[I={{I}_{0}}+{{I}_{0}}+2\sqrt{{{I}_{0}}}\sqrt{{{I}_{0}}}\cos \phi \] |
\[\frac{4{{I}_{0}}}{4}=2{{I}_{0}}+2{{I}_{0}}\cos \phi \] |
\[\therefore \cos \phi =-\frac{1}{2}\Rightarrow \phi =\frac{2\pi }{3},\frac{4\pi }{3}........\] |
and \[\phi =\frac{2\pi }{\lambda }\Delta x\] |
\[\Delta {{x}_{at}}o=(\mu -1)t\] |
\[\phi =\frac{2\pi }{\lambda }(\mu -1)t\] |
\[\phi =\frac{4\pi }{3}\] |
\[\frac{4\pi }{3}=\frac{2\pi }{\lambda }(\mu -1)t\] |
Put \[t=\lambda \] |
\[\frac{2}{3}=\left( \frac{\mu -1}{\lambda } \right)\lambda \] |
\[\mu =\frac{5}{3}\] |
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