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n identical coherent isotropic point sources each having power P are kept symmetrically on the periphery of a circle given by the equation $x^{2} + y^{2} = R^{2} .$ The resultant intensity detected by a detector placed at $(0, 0, R)$ is $I_{1}$ and the resultant intensity at $(0, 0, 2 R)$ is $I_{2} .$ The ratio $\frac{I_{1}}{I_{2}}$ is

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> 1

$\frac{2}{5}$

$\frac{1}{2}$

answer is D.

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Detailed Solution

Resultant intensity at the given points will be directly proportional to intensity due to each source at those points which in turn inversely proportional to square of the distances from sources

$\frac{I_{1}}{I_{2}} = {(\frac{r_{2}}{r_{1}})}^{2} = {(\frac{\sqrt{5} R}{\sqrt{2} R})}^{2} \Rightarrow \frac{I_{1}}{I_{2}} = \frac{5}{2} > 1$

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