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Two sources S1 and S2 emitting light of ...

Two sources `S_1 and S_2` emitting light of wave length 600 nm are placed a distance `1.0x10^-2` cm apart. A detector can be moved on the litre line `S_1P` which is perpendicular to `S_1S_2`. a.What would be the minimum and maximum path differrence at the detector as it is moved alog the line `S_1P`? b. Locate the position of the farthest minimum detect.

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a. The situation is shown in ure. The path difference is maximum when the detector is just at the position of `S_1` and its value is equal to `d=1.0xx10^-2` cm.The path difference is minimum when the detector is at a large distance from `S_1`. The path difference is then close to zero.
b. The farthest minimum ocurs at a point P where the path difference is `lamda/2. If S_1P=D`.
`S_2P-S_1P=lamda/2`
`or sqrt(D^2+d^2)-D=lamda/2`
or, `D^2+d^2=(D+lamda/2)^2`
`or, d^2=Dlamda+lamda^2/4`
or `D=d^2/lamda-lamda/4`
`=((1.0xx10^-4m)^2)/(600xx10^-9m)-150xx10^-9m=1.7cm`
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