InterviewSolution
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InterviewSolution
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An interference is observed due to two coherent sources `S_(1)` placed at origin and `S_(2)` placed at (0, 3l, 0). Here, `lambda` is the wavelength of the sources. Both sources are having equal intensity `I_(0)`. A detector D is moved along the positive x-axix. Find x-coordinates on the x-axis (exchange `x = 0` and `x = OO`).A. `x = 4 lambda`B. `x = 7 lambda//4`C. `x = 5 lambda//4`D. `x = 3 lambda` |
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Answer» Correct Answer - a.,c At ` x = 0`, path difference is `3 lambda`. Hence,third-order maximum will be obtained. At `x = oo`, path difference is zero. Hence, zero-order maxima is obtained. In between, first - and second-order maxima 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) + 9 lambda^(2)) = x + lambda` Squaring this, we get `x^(2) + 9 lambda^(2) = x^(2) + lambda^(2) + 2 x lambda` Solving this, we get `x = 4 lambda` Second-order maxima: `S_(2) P - S_(1) P = 2 lambda` or `sqrt(x^(2) + 9 lambda^(2)) - x = 2 lambda` or ` sqrt( x^(2) + 9 lambda^(2)) = (x + 2 lambda)` Squaring both sides, we get `x^(2) + 9 lambda^(2) = x^(2) + 4 lambda^(2) + 4 x lambda` Solving this, we get `x = (5)/(4) lambda = 1.25 lambda` Hence, the desired x-corrdinates are `x = 1.25 lambda` and `x = 4 lambda` |
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