A) zero
B) increased by \[6479\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) increased by \[589\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) decreased by \[589\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]
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, \[\frac{\Delta \theta }{\theta }=10%,\lambda =5890\,\overset{\text{o}}{\mathop{\text{A}}}\,\] \[\Delta \lambda =\frac{10}{100}\times 5890=589\,\overset{\text{o}}{\mathop{\text{A}}}\,\] Hence, fringe width increases by \[589\overset{\text{o}}{\mathop{\text{A}}}\,.\]You need to login to perform this action.
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