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Q.

In the fig. below, P and Q are two equally intense coherent sources emitting radiation of wavelength 20 m. The separation between P and Q is 5m and the phase of P is ahead of that of Q by  900. A, B and C are three distinct points of observation, each equidistant from the midpoint of PQ. The intensities of radiation at A, B, C will be in the ratio :

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a

2 : 1 : 0

b

0 : 1 : 4

c

4 : 1 : 0

d

0 : 1 : 2

answer is A.

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Detailed Solution

λ=20   mPQ=λ4          ,Δϕ=900​At A, ​Path diff = PA−QA=5m=PQ=λ4 ​Phase diff =2πλ×λ4 =π2​here, Q is ahead of P geometrically.And intrinsically the phase of P is ahead of that of Q by π2​So, Total phase diff at A =△ϕ=π2−π2=0​Resultant intensity=I=4I0cos2△ϕ2=4I0 MaximaAt C, ​Path diff = QC−PC=5m=PQ=λ4 ​Phase diff =2πλ×λ4 =π2​here, P is ahead of Q geometrically.And intrinsically the phase of P is ahead of that of Q by π2​So, Total phase diff at C =△ϕ=π2+π2=π​∴Resultant intensity=I=4I0cos2△ϕ2=0  MinimaAt B, ​Path diff = PB−QB=0​Phase diff =0​here, Q is same as P geometrically.​And intrinsically the phase of P is ahead of that of Q by π2So, Total phase diff at B =△ϕ=π2​Resultant intensity=I=4I0cos2△ϕ2=2I0=Imax2 ​​Thus, Intensity ratio=4I0 : 2I0 :0= 2 : 1 : 0
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