In YDSE, if the sources are incoherent the intensity on the screen is 13 $I_{o}$ when these sources are coherent the minimum intensity on the screen is $I_{o}$ .if maximum intensity produced by these coherent sources on the screen is $n I_{0}$ . Find n

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answer is 25.

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Detailed Solution

Given that, in YDSE , if the sources are incoherent , the intensity on the screen is $13 I_{0}$
When these sources are coherent, the minimum intensity on the screen is $I_{o}$ . if the maximum intensity produced by these coherent sources on the screen is $n I_{0}$ , we have to find n
For incoherent sources ,we just add the interfering intensities to get the resultant intensity.
So, $I_{1} + I_{2} = 13 I_{0.......... (i)}$
Also, for coherent sources, the minimum intensity is
${(\sqrt{I_{1}} - \sqrt{I_{2}})}^{2} = I_{0} \Rightarrow I_{1} + I_{2} - 2 \sqrt{I_{1}} \sqrt{I_{2}} = I_{0}$
$\Rightarrow 13 I_{0} - 2 \sqrt{I_{1}} \sqrt{I_{2}} = I_{0}$ (from(i))
$2 \sqrt{I_{1}} \sqrt{I_{2}} = 12 I_{0} ......... (i i)$
For coherent sources, the maximum intensity is $I_{\max} = I_{1} + I_{2} + 2 \sqrt{I_{1}} \sqrt{I_{2}}$
$\Rightarrow I_{\max} = 13 I_{0} + 12 I_{0} = 25 I_{0}$ from (i) and (ii) )