A) \[5\lambda \]
B) \[3\lambda /4\]
C) \[2\,\lambda \]
D) \[11\lambda /2\]
Correct Answer: D
Solution :
| For destructive interference: |
| \[\operatorname{Path}\,\,difference=\,\,{{S}_{1}}P-{{S}_{2}}P=\,\,(2n-1)\,\lambda /2\] |
| For \[\operatorname{n}=1,\,\,\,\,{{S}_{1}}P\,-{{S}_{2}}P=(2\times 1-1)\,\lambda /2=\,\,\lambda /2\] |
| \[\operatorname{n}=2,\,\,{{S}_{1}}P\,-{{S}_{2}}P=\,\,(2\times 2-1)A/2=3/2\] |
| \[\operatorname{n}=3, {{S}_{1}}P\,-{{S}_{2}}P=\,\,\left( 2\times 3-1 \right)\lambda /2=5\lambda /2\] |
| \[\operatorname{n}=4,\,\,{{S}_{1}}P\,-{{S}_{2}}P=\,\,(2\times 4-1)\lambda /2=\,\,7\lambda /2\] |
| \[\operatorname{n}=5,\,\,{{S}_{1}}P\,-{{S}_{2}}P=\,\,(2\times 5-1)\lambda /2\,\,=\,\,9\lambda /2\] |
| \[\operatorname{n}=6,\,\,{{S}_{1}}P\,-{{S}_{2}}P=\,\,(2\times 6-1)\lambda /2=\,\,11\lambda /2\] |
| So, destructive pattern is possible only for path difference \[=\,\,11\,\lambda /2.\] |
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