A) zero
B) increased by \[6479\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) increased by \[589\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) decreased by \[589\overset{\text{o}}{\mathop{\text{A}}}\,\]
Correct Answer: C
Solution :
Angular fringe width\[\theta =\frac{\beta }{D}=\frac{\lambda }{2d}\] \[\therefore \] \[\frac{\theta '}{\theta }=\frac{\lambda '}{\lambda }\] or \[\frac{\theta '-\theta }{\theta }=\frac{\lambda '-\lambda }{\lambda }\] \[\therefore \] \[\Delta \lambda =\frac{\Delta \theta }{\theta }\lambda \] Given, \[\frac{\Delta \theta }{\theta }=10%,\,\,\lambda =5890{\AA}\] \[\Delta \lambda =\frac{10}{1000}\times 5890=589{\AA}\] Hence, fringe width increases by 589A.
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