A) \[\frac{{{n}_{1}}\lambda }{2{{n}_{2}}}\]
B) \[\frac{{{n}_{1}}\lambda }{4{{n}_{2}}}\]
C) \[\frac{\lambda }{4{{n}_{2}}}\]
D) \[\frac{\lambda }{2{{n}_{2}}}\]
Correct Answer: B
Solution :
[b] Equation of path difference form maxima in transmission (or weak reflection) \[\Delta {{P}_{opt}}=2{{n}_{2}}L=\frac{{{\lambda }_{vacuum}}}{2},\frac{3{{\lambda }_{vacuum}}}{2}....\] \[\Rightarrow 2\left( \frac{{{n}_{2}}}{{{n}_{1}}} \right)\] \[L=\frac{\lambda }{2}\], \[\frac{3\lambda }{2}......\Rightarrow L=\frac{\lambda }{4{{n}_{2}}}\] (notice that \[\lambda \]= wavelength in medium is related to \[{{\lambda }_{vacuum}}\]as, \[{{\lambda }_{vacuum}}={{n}_{1}}\lambda \])
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