A) \[6.738\times {{10}^{-5}}cm\]
B) \[5.7\times {{10}^{-5}}cm\]
C) \[4\times {{10}^{-5}}cm\]
D) \[2.8\times {{10}^{-5}}cm\]
Correct Answer: A
Solution :
[a] In this case, both the rays suffere a phase change of \[180{}^\circ \] and the conditions for destructive interference is \[2nd=\left( m+\frac{1}{2} \right){{\lambda }_{1}}\] and \[2nd=\left( m+\frac{3}{2} \right){{\lambda }_{2}}\] \[\therefore \,\,\,\frac{m+\frac{1}{2}}{m+\frac{3}{2}}=\frac{{{\lambda }_{2}}}{{{\lambda }_{1}}}=\frac{5000}{700}=\frac{5}{7}\] and \[d=\frac{\left( m+\frac{1}{2} \right){{\lambda }_{1}}}{2n}=\frac{2.5\times 7000}{2\times 1.3}\] \[=6.738\times {{10}^{-5}}cm\]
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