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An interference is observed due to two coherent sources S_1placed at origin and S_2placed at (0,3lamda,0). Here lamdais the wavelength of the sources. A detector Dis moved along the positive X-axis. Find x-coordinates (excluding x = 0 and x = oo) where maximum intensity is observed. |
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Answer» <P> Solution :At x = 0, path difference is `3lamda` . 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_1P - S_1P = LAMDA " or "sqrt(x^2 + 9 lamda^2) - x = lamda ` or`sqrt(x^2 + 9 lamda^2) = x +lamda`Squaring both SIDES, we get `x^2 = 9lamdaa^2 = x^2 + lamda^2 + 2x lamda`SOLVING this, we get `x = 4 lamda` Second order maxima: `S_2 P - S_1 P = 2 lamda` or`sqrt(x^2 + 9 lamda^2) - x = 2 lamda " or" sqrt(x^2 + 9 lamda^2) = (x + 2 lamda)` Squaring both sides, we get ` x^2 + 9 lamda^2 =x^2 +4 lamda^2 + 4X lamda` Solving, we get` x = 5/4 lamda = 1.25 lamda` Hence, the desired x coordinates are, `x = 1.25 lamda` and x = `4 lamda` |
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