A) \[38.2{{A}^{o}}\]
B) \[68.32{{A}^{o}}\]
C) \[5892.{{A}^{o}}\]
D) \[528.32{{A}^{o}}\]
Correct Answer: C
Solution :
[c] Fringe shift when a sheet of thickness t and refractive index u is introduced in path of one of interfering waves is \[\Delta x=\frac{Dt(\mu -1)}{d}=\frac{D\times 1.964\times {{10}^{-6}}(1.6-1)}{d}...(i)\] The distance between two maxima where mica sheet is remove and the distance between the slits and the screen is doubled \[=\frac{\lambda (2D)}{d}\] ...(ii) Given that the value in eq. (i) and eq. (ii) are equal \[\therefore \,\,\,\frac{D\times 1.964\times {{10}^{-6}}0.6}{d}=\frac{\lambda \times 2D}{d}\] \[\Rightarrow \,\,\lambda =\frac{1.964\times {{10}^{-6}}\times 0.6}{2}\] \[=0.5896\times {{10}^{-6}}m=5892\overset{o}{\mathop{A}}\,\]
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