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=900At A, Path diff = PA−QA=5m=PQ=λ4 Phase diff =2πλ×λ4 =π2here, Q is ahead of P geometrically.And intrinsically the phase of P is ahead of that of Q by π2So, Total phase diff at A =△ϕ=π2−π2=0Resultant intensity=I=4I0cos2△ϕ2=4I0 MaximaAt C, Path diff = QC−PC=5m=PQ=λ4 Phase diff =2πλ×λ4 =π2here, P is ahead of Q geometrically.And intrinsically the phase of P is ahead of that of Q by π2So, Total phase diff at C =△ϕ=π2+π2=π∴Resultant intensity=I=4I0cos2△ϕ2=0 MinimaAt B, Path diff = PB−QB=0Phase diff =0here, 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=π2Resultant intensity=I=4I0cos2△ϕ2=2I0=Imax2 Thus, Intensity ratio=4I0 : 2I0 :0= 2 : 1 : 0