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An interference is observed due to two coherent sources S_(1) placed at origion and S_(2) placed at (0, 3lambda, 0). Here lambda is the wavelength of the sources. A detector D is moved along the positive x-axis. Find x-coordinates on the x-axis (excluding x= 0 and x= oo) where maximum intensity is observed. |
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Answer» <P> Solution :At x=0, path difference is `3lambda`. Hence, third order maxima will be obtained. At `x=oo`, path difference is ZERO. Hence, zero order maxima is obtained. In between first and second order maximas will be obtained.First order maxima : `S_(2)P-S_(1)P= lambda` (or) `sqrt(x^(2)+9lambda^(2))-x= lambda` or `sqrt(x^(2)+9lambda^(2))= x+ lambda` SQUARING both sides, we get `x^(2)+9lambda^(2)= x^(2)+lambda^(2)+2x lambda` SOLVING this, we get `x= 4 lambda` Second order maxima : `S_(2)P-S_(1)P= 2 lambda` (or) `sqrt(x^(2)+9lambda^(2))- 2lambda"(or) "sqrt(x^(2)+9lambda^(2))= (x+2lambda)` Squaring both sides, we get `x^(2)+9lambda^(2)= x^(2)+4lambda^(2)+ 4x lambda` Solving, we get `x= (5)/(4)lambda= 1.25 lambda` Hence, the desired x coordinates are, `x= 1.25 lambda" and "x= 4lambda`.  .
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