A) \[\text{8 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\,\text{rad}\]
B) \[\text{6 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\,\text{rad}\]
C) \[\text{4 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\,\text{rad}\]
D) \[\text{16 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\,\text{rad}\]
Correct Answer: A
Solution :
Destructive interference occurs when the path difference is an odd multiple of\[\lambda /2.\] i.e., \[\frac{xd}{D}=\frac{(2n-1)\lambda }{2}\] Angular width of first dark fringe is \[\frac{2x}{D}=\frac{2(2n-1)\lambda }{2d}\] Given, \[n=1,\lambda =4800\overset{\text{o}}{\mathop{\text{A}}}\,=4800\times {{10}^{-10}}m,\] \[d=0.6\,mm=0.6\times {{10}^{-3}}\,m\] \[\therefore \] \[\frac{2x}{D}=\frac{2(2\times 1-1)\times 4800\times {{10}^{-10}}}{2\times 0.6\times {{10}^{-3}}}\] \[=8\times {{10}^{-4}}\,\,rad\]
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