A) \[1.1\times {{10}^{-2}}cm\]
B) \[1\times {{10}^{-2}}cm\]
C) \[3.28\times {{10}^{6}}cm\]
D) \[11\times {{10}^{-2}}cm\]
E) None of the Above
Correct Answer: E
Solution :
: Here, Fringe width, \[\beta =0.002cm=2\times {{10}^{-3}}cm\] Distance of nth dark fringe from centre \[{{x}_{n}}=\left( n-\frac{1}{2} \right)\frac{\lambda D}{d}\]where \[n=1,2,3,....\] As \[\beta =\frac{\lambda D}{d}\] \[\therefore \] \[{{x}_{n}}\left( n-\frac{1}{2} \right)\beta \] For 5th dark fringe, \[n=5\] \[\therefore \] \[{{x}_{5}}=\left( 5-\frac{1}{2} \right)\beta =\frac{9}{2}\beta =\frac{9}{2}\times 2\times {{10}^{-3}}cm\] \[=9\times {{10}^{-3}}cm\] * None of the given options is correct.
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