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Ratio waves originating from sources S(1...

Ratio waves originating from sources `S_(1)` and `S_(2)` having zero phase difference and common wavelength `lambda` will show completely destructive interference at a point `P` is `S_(1)P-S_(2)P` is

A

`5lambda`

B

`3lambda//4`

C

`2lambda`

D

`11lambda//2`

Text Solution

Verified by Experts

For destructive interference:
Path difference =`S_(1)P-S_(2)P=(2n-1)lambda//2`
`n=1,S_(1)P-S_(2)P=(2xx1-1)lambda//2=lambda//2`
`n=2,S_(1)P-S_(2)P=(2xx2-1)lambda//2=3lambda//2`
`n=3,S_(1)P-S_(2)P=(2xx3-1)lambda//2=5lambda//2`
`n=4,S_(1)P-S_(2)P=(2xx4-1)lambda//2=7lambda//2`
`n=5,S_(1)P-S_(2)P=(2xx5-1)lambda//2=9lambda//2`
`n=6,S_(1)P-S_(2)P=(2xx6-1)lambda//2=11lambda//2`
So,destructive pattern is possible only for path difference=`11lambda//2`.
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