An interference is observed due to two coherent sources separated by a distance 5 $λ$ along y-axis, where $λ$ is the wavelength of light. One source lies on y=0, the other source lies on y=5 $λ$ . A detector D is moved along the positive x-axis. The number of points on the x-axis excluding the points x = 0 and x = $\infty$ at which resultant intensity will be maximum, are :

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$\infty$

Zero

answer is A.

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Detailed Solution

$△ A B D \begin{aligned} (A D)^{2} = (A B)^{2} + (B D)^{2} \\ \Rightarrow (A P + P D)^{2} = (A B)^{2} + (B D)^{2} \\ A P i s t h e p a t h d i f f e r e n c e \end{aligned} \Rightarrow {(n λ + x_{n})}^{2} = (5 λ)^{2} + {(x_{n})}^{2} \Rightarrow x_{n} = \frac{25 λ^{2} - n^{2} λ^{2}}{2 n λ} F o r n = 1; x_{n} = 12 λ n = 2; x_{n} = 5.25 λ n = 3; x_{n} = 2.67 λ n = 4; x_{n} = 1.125 λ F o r n = 5, x_{n} = 0$